item: #1 of 150 id: jacodesmath-1 author: Bayram, Ayşegül ; Siap, Irfan title: Cyclic and constacyclic codes over a non-chain ring date: 2014-09-15 words: 5615 flesch: 91 summary: Cyclic Codes over Rp A very significant and well know class of linear codes is the class of cyclic codes which plays a crucial role in coding theory due to their easy implementation. However, the study on non-chain rings has proved to be challenging due to the algebraic structure of these rings which does not allow to give a nice and compact presentation of linear codes over these rings. keywords: codes; constacyclic; cyclic; ideals; linear; ring cache: jacodesmath-1.pdf plain text: jacodesmath-1.txt item: #2 of 150 id: jacodesmath-100 author: Bouchat, Rachelle R.; Brown, Tricia Muldoon title: Fibonacci numbers and resolutions of domino ideals date: 2019-05-15 words: 6138 flesch: 73 summary: 63–74 Received: 23 March 2018 Accepted: 12 March 2019 0 Journal of Algebra Combinatorics Discrete Structures and Applications Fibonacci numbers and resolutions of domino ideals Research Article Rachelle R. Bouchat, Tricia Muldoon Brown Abstract: This paper considers a class of monomial ideals, called domino ideals, whose generating sets correspond to the sets of domino tilings of a 2 × n tableau. It is well-known that the number of domino tilings of a 2 × n tableau is given by a Fibonacci number. keywords: betti; depth; domino; monomial; numbers; sequence; set; tilings cache: jacodesmath-100.pdf plain text: jacodesmath-100.txt item: #3 of 150 id: jacodesmath-101 author: Jitman, Somphong; Ling, San title: Self-dual and complementary dual abelian codes over Galois rings date: 2019-05-15 words: 10235 flesch: 78 summary: Clearly, {0} and GR(pr,s)[P ] are Euclidean complementary dual abelian codes in GR(pr,s)[P]. The number of Euclidean complementary dual abelian codes in GR(pr,s)[P ] is 2. keywords: abelian; abelian codes; codes; dual; dual abelian; euclidean; finite; gr(pr; group; s)[g; self cache: jacodesmath-101.pdf plain text: jacodesmath-101.txt item: #4 of 150 id: jacodesmath-102 author: Hamzekolaee, Ali Reza Moniri; Talebi, Yahya title: Coretractable modules relative to a submodule date: 2019-05-15 words: 5708 flesch: 80 summary: If in the definition of a coretractable module M, we fix a submodule N and focus just on nonzero homomorphisms from M/K to M where K 6= M contains N, we have a special generalization of coretractable modules. Then K is essential in M denoted by K ≤e M, if L∩K 6= 0 keywords: coretractable; module; submodule cache: jacodesmath-102.pdf plain text: jacodesmath-102.txt item: #5 of 150 id: jacodesmath-103 author: Ban, Jung-Chao; Chang, Chih-Hung title: Complexity of neural networks on Fibonacci-Cayley tree date: 2019-05-15 words: 7227 flesch: 73 summary: 2010 MSC: 37A35, 37B10, 92B20 Keywords: Neural networks, Learning problem, Cayley tree, Separation property, Entropy 1. A Fibonacci-Cayley tree (Fibonacci tree) t over a finite alphabet A is a function from ΣA to A; in other words, a Fibonacci tree is a pattern whose support is the Fibonacci lattice ΣA. keywords: cayley; entropy; fibonacci; fibonacci tree; finite; networks; neural; shift; tree cache: jacodesmath-103.pdf plain text: jacodesmath-103.txt item: #6 of 150 id: jacodesmath-104 author: Bikov, Dusan; Bouyukliev, Iliya; Bouyuklieva, Stefka title: Bijective S-boxes of different sizes obtained from quasi-cyclic codes date: 2019-09-15 words: 6894 flesch: 77 summary: There are different methods to construct quasi-cyclic codes. To connect the codes with S-boxes, we consider the binary simplex codes as quasi-cyclic codes. keywords: boxes; code; matrix; qcs cache: jacodesmath-104.pdf plain text: jacodesmath-104.txt item: #7 of 150 id: jacodesmath-105 author: McCullough, Jason; Newman, Heather title: Asymptotically good homological error correcting codes date: 2019-10-15 words: 5234 flesch: 77 summary: Since the Moore bound gives a logarithmic bound on the girth of a graph in terms of the number of edges and vertices, it follows that one cannot define asymptotically good families of codes from cycle codes of graphs. By applying recent work in [4] and [2], we show in Theorem 4.2 that one can define asymptotically good families of codes from cycle codes of simplicial complexes of dimension two or higher. keywords: codes; complex; dimk; theorem cache: jacodesmath-105.pdf plain text: jacodesmath-105.txt item: #8 of 150 id: jacodesmath-106 author: Ozbek, Ibrahim; Temiz, Fatih; Siap, Irfan title: A generalization of the Mignotte's scheme over Euclidean domains and applications to secret image sharing date: 2019-10-15 words: 6703 flesch: 72 summary: We also construct threshold secret image sharing schemes based on generalization of Mignotte’s scheme over polynomial rings. 2010 MSC: 11K31, 94A08, 94A62, 13F07 Keywords: Mignotte sequences, Secret image sharing, Secret sharing scheme, Euclidean domain 1. keywords: image; polynomials; scheme; secret; shadow; sharing cache: jacodesmath-106.pdf plain text: jacodesmath-106.txt item: #9 of 150 id: jacodesmath-107 author: Bag, Tushar; Islam, Habibul; Prakash, Om; Upadhyay, Ashish K. title: A note on constacyclic and skew constacyclic codes over the ring $\mathbb{Z}_{p} [u,v]/\langle u^2-u,v^2-v,uv-vu\rangle$ date: 2019-09-15 words: 5587 flesch: 89 summary: 6(3) • 163–172 Received: 20 October 2018 Accepted: 21 August 2019 Journal of Algebra Combinatorics Discrete Structures and Applications A note on constacyclic and skew constacyclic codes over the ring Zp[u, v]/〈u2 Finally, as an application of our study, we compute several non trivial linear codes by using the Gray images of (1 + (p− 2)u)-constacyclic codes over this ring R. 2010 MSC: 94B05, 94B15 , 94B60 Keywords: Constacyclic codes, Skew constacyclic codes, Gray map, Quasi-cyclic codes 1. keywords: + d0; c0 +; codes; length cache: jacodesmath-107.pdf plain text: jacodesmath-107.txt item: #10 of 150 id: jacodesmath-108 author: Aydin, Nuh; Yildiz, Bahattin title: Editor’s Note. Special Issue Algebraic Coding Theory: New Trends and Its Connections date: 2020-01-15 words: 558 flesch: 51 summary: In Weight distributions of some constacyclic codes over a finite field and isodual constacyclic codes, Singh describes the weight distribution of a family of constacyclic codes over Fq. In Zq(Zq + uZq)-linear skew constacyclic codes, Melakhessou et al. consider Zq(Zq+uZq) skew constacyclic codes where q is a prime power and u2 = 0. keywords: codes; issue cache: jacodesmath-108.pdf plain text: jacodesmath-108.txt item: #11 of 150 id: jacodesmath-109 author: Gulliver, Aaron; Venkaiah, Vadlamudi Ch. title: Construction of Quasi-Twisted Codes and Enumeration of Defining Polynomials date: 2020-01-15 words: 7082 flesch: 91 summary: By restricting the search for good codes to the class of QT codes, and using a stochastic heuristic, codes with high minimum distance can be found with a reasonable amount of computational effort. Defining polynomials The construction of QT codes requires a representative set of defining polynomials. keywords: codes; number; polynomials; t(b cache: jacodesmath-109.pdf plain text: jacodesmath-109.txt item: #12 of 150 id: jacodesmath-11 author: Dinh, Hai Q.; Li, Chengju; Yue, Qin title: Recent progress on weight distributions of cyclic codes over finite fields date: 2015-01-15 words: 14273 flesch: 79 summary: If we only give g1 and g2, we mean that the dual of cyclic code has two zeros and the product of the minimal polynomials of g1 and g2 over Fq is the check polynomial of such cyclic code. Recent progress on weight distributions of cyclic codes over finite fields∗ Research Article Hai Q. Dinh1∗∗, Chengju Li2§, Qin Yue2∗∗∗ 1. keywords: codes; constacyclic; cyclic; cyclic codes; fields; finite; mod; n =; theorem; theory; weight; weight cyclic; weight distributions cache: jacodesmath-11.pdf plain text: jacodesmath-11.txt item: #13 of 150 id: jacodesmath-110 author: Singh, Manjit title: A Class of Constacyclic Codes Containing Formally Self-dual and Isodual Codes date: 2020-01-15 words: 6871 flesch: 83 summary: [5] T. Blackford, Isodual constacyclic codes, Finite Fields Appl. A class of constacyclic codes containing formally self-dual and isodual codes Research Article Manjit Singh Abstract: In this paper, we investigate a class of constacyclic codes which contains isodual codes and formally self-dual codes. keywords: codes; dual; k+r; n−r cache: jacodesmath-110.pdf plain text: jacodesmath-110.txt item: #14 of 150 id: jacodesmath-111 author: Haymaker, Kathryn; O'Pella, Justin title: Locally Recoverable Codes From Planar Graphs date: 2020-01-15 words: 7608 flesch: 75 summary: We prove that the minimum distance of planar graph LRCs is equal to the girth of the graph, and we also establish a new bound on the rate of planar graph edge codes. [7] M. Meringer, Regular planar graphs, available online at http://www.mathe2.uni-bayreuth.de/ markus/reggraphs.html, accessed 2009. keywords: code; degree; edges; graph; rate; vertices cache: jacodesmath-111.pdf plain text: jacodesmath-111.txt item: #15 of 150 id: jacodesmath-112 author: Dougherty, Steven T.; Gildea, Joe; Korban, Adrian title: G-codes over Formal Power Series Rings and Finite Chain Rings date: 2020-01-15 words: 9060 flesch: 89 summary: Introduction One of the most widely studied families of codes is the family of cyclic codes. Moreover, it generalizes the notion of cyclic codes by considering codes whose automorphism group contains the arbitrary group G as a subgroup. keywords: code; dual; finite; group; matrix; ring; self cache: jacodesmath-112.pdf plain text: jacodesmath-112.txt item: #16 of 150 id: jacodesmath-113 author: Lieb, Julia; Pinto, Raquel title: Constructions of MDS Convolutional Codes Using Superregular Matrices date: 2020-01-15 words: 5729 flesch: 82 summary: The theory of convolutional codes is more involved than the theory of block codes and there are not many known constructions of MDS convolutional codes. + 1, since [G1 G0] ( ul−1 ul ) is a nonzero linear combination of δ columns of G1 and k − δ columns of G0 and n ≥ keywords: codes; convolutional; matrix; mds cache: jacodesmath-113.pdf plain text: jacodesmath-113.txt item: #17 of 150 id: jacodesmath-114 author: Melakhessou, Ahlem; Aydin, Nuh; Hebbache, Zineb; Guenda, Kenza title: Z_q(Z_q+uZ_q)-Linear Skew Constacyclic Codes date: 2020-01-15 words: 8041 flesch: 88 summary: = Cα ×Cβ is a skew λ−constacyclic code over ZqR then by Theorem 3.8, we have that Cα is a constacyclic codes over Zq and Cβ is skew constacyclic codes over R. Further, from Theorem 5.4, we have that, if Cβ is skew constacyclic code over R then φ(Cβ) is a quasi twisted code of length 2β over Zq of index 2. Finally, we have generalized these codes to double skew constacyclic codes over ZqR. 2010 MSC: 94B15, 94B60 Keywords: Linear codes, Skew constacyclic codes, ZqZq[u]− linear skew constacyclic codes, Bounds 1. keywords: codes; constacyclic; f(x; linear; r[x; ring; skew; zqr cache: jacodesmath-114.pdf plain text: jacodesmath-114.txt item: #18 of 150 id: jacodesmath-116 author: Ghorbani, Vahid; Azadi, Ghodratollah; Azanchiler, Habib title: Generalization of pinching operation to binary matroids date: 2020-09-06 words: 6593 flesch: 83 summary: The matroids N1 and N2, defined as in definitions 5.6 and 5.7, are extensions of the notions of subdivision and vertex identification from graphs to connected binary matroids. 7(3) • 247–258 Received: 14 April 2020 Accepted: 1 May 2020 Journal of Algebra Combinatorics Discrete Structures and Applications Generalization of pinching operation to binary matroids Research Article Vahid Ghorbani, Ghodratollah Azadi, Habib Azanchiler Abstract: In this paper, we generalize the pinching operation on two edges of graphs to binary matroids and investigate some of its basic properties. keywords: binary; matroid; mpxy; operation; pinching cache: jacodesmath-116.pdf plain text: jacodesmath-116.txt item: #19 of 150 id: jacodesmath-117 author: Ishizuka, Keita title: Classification of optimal quaternary Hermitian LCD codes of dimension 2 date: 2020-09-06 words: 3762 flesch: 85 summary: A generator matrix of the code C is any matrix whose rows form a basis of C. Moreover, a generator matrix of the Hermitian dual code C⊥h is said to be a parity check matrix of C. Given a matrix G, we denote the transpose of G by GT and the conjugate of G by G. Hermitian linear complementary dual codes, Hermitian LCD codes for short, are codes whose intersections with their Hermitian dual codes are trivial. Therefore, it is difficult to extend our method to classify Hermitian LCD codes of larger dimensions. keywords: codes; hermitian; lcd cache: jacodesmath-117.pdf plain text: jacodesmath-117.txt item: #20 of 150 id: jacodesmath-119 author: Bono, Nanami; Fujii, Maya; Maruta, Tatsuya title: On optimal linear codes of dimension 4 date: 2021-05-16 words: 11826 flesch: 91 summary: To prove this, we need to show the existence of a [gq(4,d) + 1, 4,d]q code for d = q3 − 2q2 by Theorem 1.2 (b). We recall that the multiset for a [2q2 − q − 1, 3, 2q2 − 3q]q code with q ≥ 5 consists of two copies of PG(2,q) with three non-concurrent lines deleted [16]. keywords: code; lemma; line; plane; spectrum; t = cache: jacodesmath-119.pdf plain text: jacodesmath-119.txt item: #21 of 150 id: jacodesmath-12 author: Eubanks-Turner, Christina; Li, Aihua title: Graphical properties of the bipartite graph of Spec(Z[x])\{0} date: 2015-01-15 words: 4796 flesch: 80 summary: Many basic graph theory properties of GZ can be obtained from the ring theory properties of Spec(Z[x]), for example, Proposition 2.7 (2) and (3) shown above. The work in this paper gives a set of graph theoretic properties of the derived graph GZ by Spec(Z[x]) \ {0} as an infinite bipartite graph. keywords: graph cache: jacodesmath-12.pdf plain text: jacodesmath-12.txt item: #22 of 150 id: jacodesmath-126 author: Korban, Adrian title: Composite G-codes over formal power series rings and finite chain rings date: 2021-05-16 words: 7737 flesch: 88 summary: Composite G-codes In this section, we define a circulant matrix, give the definitions for group rings and introduce composite G- codes. Let C be a finitely generated linear code over R∞. Then the generator matrix of code C is permutation equivalent to the following standard form generator matrix. keywords: code; composite; finite; matrix; results; rings; ω(v cache: jacodesmath-126.pdf plain text: jacodesmath-126.txt item: #23 of 150 id: jacodesmath-129 author: Gildea, Joe; Kaya, Abidin; Tylyshchak, Alexander; Yildiz, Bahattin title: A Modified Bordered Construction for Self-dual Codes From Group Rings date: 2020-05-07 words: 6473 flesch: 92 summary: + (173063 − 22β) y16 + · · · The code with weight enumerator for γ = 1,β = 416 is constructed in [13]. = ∑ i,j αgiβgjgigj. keywords: codes; dual; self cache: jacodesmath-129.pdf plain text: jacodesmath-129.txt item: #24 of 150 id: jacodesmath-13 author: Martinez-Moro, Edgar; Özadam, Hakan; Özbudak, Ferruh; Szabo, Steve title: On a class of repeated-root monomial-like abelian codes date: 2015-05-15 words: 4447 flesch: 89 summary: ,xn], where cβ ∈ Fpa \{0}, β = (β1, . . . ,βn) and (x1 −c1)N1 (x2 −c2)N2 · · ·(xn−cn)Nn divides (x1 −c1)β1 (x2 − c2) β2 · · ·(xn − cn)βn for every β ∈ ψ. β1 (x2 − c2)β2 · · ·(xn−1 − cn−1)βn−1 +(xn − cn) ∑ β∈ψ keywords: codes; fpa; let cache: jacodesmath-13.pdf plain text: jacodesmath-13.txt item: #25 of 150 id: jacodesmath-130 author: Sedghi, Shaban; Shobe, Nabi title: Degree Distance and Gutman Index of Two Graph Products date: 2020-05-07 words: 6708 flesch: 97 summary: Let DG be distance matrix of graph G = G1 ∨G2. Let DG be distance matrix of graph G = G1 ∨G2. keywords: b),(c; d)}⊆v1×v2; dg1; dg2; graph cache: jacodesmath-130.pdf plain text: jacodesmath-130.txt item: #26 of 150 id: jacodesmath-131 author: Ferrari, Agnaldo José; De Andrade, Antonio Aparecido; De Araujo, Robson Ricardo; Interlando, José Carmelo title: Trace Forms of Certain Subfields of Cyclotomic Fields and Applications date: 2020-05-07 words: 10720 flesch: 90 summary: 7(2) • 141–160 Received: 7 October 2019 Accepted: 4 December 2019 Journal of Algebra Combinatorics Discrete Structures and Applications Trace forms of certain subfields of cyclotomic fields and applications∗ Research Article Agnaldo José Ferrari, Antonio Aparecido de Andrade, Robson Ricardo de Araujo, José Carmelo Interlando Abstract: In this work, we present a explicit trace forms for maximal real subfields of cyclotomic fields as tools for constructing algebraic lattices in Euclidean space with optimal center density. We also obtain a closed formula for the Gram matrix of algebraic lattices obtained from these subfields. keywords: i=1; j n; j=1; lattices; m/2−1∑ cache: jacodesmath-131.pdf plain text: jacodesmath-131.txt item: #27 of 150 id: jacodesmath-132 author: Martin, William J.; Stinson, Douglas R. title: Some Bounds Arising From a Polynomial Ideal Associated to Any t-Design date: 2020-05-07 words: 12155 flesch: 83 summary: For any pair B1,B2 ∈ B with B1 ∩ B2 = ∅, the number mi,j of blocks B ∈ B with |B ∩ B1| = i and |B ∩B2| 7(2) (2020) 161–181 Let C ⊆ X with characteristic vector c and suppose {|C ∩B| : B ∈ B} = {i1, . . . keywords: blocks; design; i(b; ideal; points; polynomials; set cache: jacodesmath-132.pdf plain text: jacodesmath-132.txt item: #28 of 150 id: jacodesmath-133 author: Rashidi, Saeedeh; Poursalavati, Nosratollah Shajareh; Tavakkoli, Maryam title: Computing the Zero Forcing Number for Generalized Petersen Graphs date: 2020-05-07 words: 3807 flesch: 83 summary: Let A be a set of initial black vertices of the graph P(n,3). Note that, r vertices can be belong to the inner cycle of generalized peterson graph 185 S. Rashidi et al. / keywords: black; graph; set; vertex; vertices cache: jacodesmath-133.pdf plain text: jacodesmath-133.txt item: #29 of 150 id: jacodesmath-134 author: Interlando, Carmelo; Khathuria, Karan; Rohrer, Nicole; Rosenthal, Joachim; Weger, Violetta title: Generalization of the Ball-Collision Algorithm date: 2020-05-07 words: 6561 flesch: 72 summary: − v1 − v2 − w1 − w2 is satisfied. keywords: algorithm; ball; collision; decoding; information; set cache: jacodesmath-134.pdf plain text: jacodesmath-134.txt item: #30 of 150 id: jacodesmath-137 author: Dela Cruz, Ben Paul Bautista; Lampos, John Mark ; Palines, Herbert ; Sison, Virgilio title: A new construction of anticode-optimal Grassmannian codes date: 2021-01-25 words: 3814 flesch: 80 summary: [4] B. Hernandez, V. Sison, Grassmannian codes as lifts of matrix codes derived as images of linear block codes over finite fields, Global Journal of Pure and Applied Mathematics 12(2) (2016) 1801–1820. [k × `] matrix code over Fq is a nonempty subset of Mk×`(Fq). keywords: code; distance; rank cache: jacodesmath-137.pdf plain text: jacodesmath-137.txt item: #31 of 150 id: jacodesmath-138 author: Ferrari, Agnaldo José; Jorge, Grasiele Cristiane; Andrade, Antonio Aparecido title: Rotated $D_n$-lattices in dimensions power of $3$ date: 2021-09-25 words: 5179 flesch: 91 summary: − − r = 6 158 A. J. Ferrari et. − − r = 10 − − − p1,p2 ∈{19,1459} r = 10 8192 r = 15 − − r = 15 − r = 12, p = 17 − − 16384 r = 16 − − r = 16 − r = 13, p = 5 − − 19683 keywords: 3r−1; lattices; − − cache: jacodesmath-138.pdf plain text: jacodesmath-138.txt item: #32 of 150 id: jacodesmath-139 author: Cengellenmis, Yasemin; Aydın, Nuh; Dertli, Abdullah title: Reversible DNA codes from skew cyclic codes over a ring of order 256 date: 2021-01-24 words: 3972 flesch: 79 summary: In [6], cyclic DNA codes over R are studied. [7] A. Dertli, Y. Cengellenmis, On cyclic DNA codes over the rings Z4 +wZ4 and Z4 +wZ4 +vZ4 +wvZ4, Biomath 6(2) (2017) 1712167. keywords: codes; cyclic; dna cache: jacodesmath-139.pdf plain text: jacodesmath-139.txt item: #33 of 150 id: jacodesmath-14 author: Soprunov, Ivan title: Lattice polytopes in coding theory date: 2015-05-15 words: 5184 flesch: 73 summary: 2(2) • 85-94 Received: 31 October 2014; Accepted: 21 February 2015 DOI 10.13069/jacodesmath.75353 Journal of Algebra Combinatorics Discrete Structures and Applications Lattice polytopes in coding theory Research Article Ivan Soprunov∗ Department of Mathematics, Cleveland State University, Cleveland, OH USA Abstract: In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. This makes toric codes a wonderful example of an interconnection between algebraic geometry (toric varieties), geometric combinatorics (lattice polytopes), and coding theory. keywords: codes; lattice; minimum; points; polytopes; toric cache: jacodesmath-14.pdf plain text: jacodesmath-14.txt item: #34 of 150 id: jacodesmath-140 author: Kaliappan, Sowndhariya ; Appu, Muthusamy title: Decomposition of product graphs into sunlet graphs of order eight date: 2021-01-25 words: 7823 flesch: 85 summary: L8 decomposition of K4 × K4,1. L8- decomposition of K4,4. keywords: decomposition; graphs; mod; x11 x cache: jacodesmath-140.pdf plain text: jacodesmath-140.txt item: #35 of 150 id: jacodesmath-141 author: Faal, Hossein Teimoori title: Clique polynomials of $2$-connected $K_{5}$-free chordal graphs date: 2021-01-24 words: 3050 flesch: 74 summary: [6] X. Li, I. Gutman, A unified approach to the first derivatives of graph polynomials, Discrete Applied Mathematics 587 (1995) 293–297. Indeed, he showed that an intersting subclass of chordal graphs has only clique roots. keywords: c(g; chordal; clique; graphs cache: jacodesmath-141.pdf plain text: jacodesmath-141.txt item: #36 of 150 id: jacodesmath-144 author: Amouzegar, Tayyebeh; Tribak, Rachid title: Some results on relative dual Baer property date: 2020-09-06 words: 5293 flesch: 85 summary: From [14, Example 3.1 and Theorem 3.4], it follows that a direct sum of dual Baer modules is not dual Baer, in general. 259–267 We conclude this paper by showing a new characterization of dual Baer modules. keywords: baer; module cache: jacodesmath-144.pdf plain text: jacodesmath-144.txt item: #37 of 150 id: jacodesmath-147 author: Morris, Joy; Smolcic, Josip title: Two families of graphs that are Cayley on nonisomorphic groups date: 2021-01-25 words: 2765 flesch: 71 summary: 2010 MSC: 05C25, 05C60 Keywords: Cayley graphs, Nonisomorphic groups 1. Cayley graphs and digraphs are a major area of study, as their symmetries lead to many useful properties in the networks they represent. keywords: cayley; group cache: jacodesmath-147.pdf plain text: jacodesmath-147.txt item: #38 of 150 id: jacodesmath-148 author: Juras, Martin; Ursul, Mihail title: On commuting probabilities in finite groups and rings date: 2022-01-13 words: 3499 flesch: 73 summary: On commuting probabilities in finite groups and rings Research Article Martin Juráš, Mihail Ursul Abstract: We show that the set of all commuting probabilities in finite rings is a subset of the set of all commuting probabilities in finite nilpotent groups of class ≤ 2. We will use the following classes of groups and rings: G the class of finite groups; Gnil the class of finite nilpotent groups; G (2) nil the class of finite nilpotent groups of class ≤ 2; R the class of finite rings; R (2) nil the class of finite nilpotent rings of class ≤ 3; 2 keywords: class; commuting; finite; group; probability; rings cache: jacodesmath-148.pdf plain text: jacodesmath-148.txt item: #39 of 150 id: jacodesmath-15 author: Pirzada, S.; Chat, Bilal A.; Dar, Farooq A. title: Graphical sequences of some family of induced subgraphs date: 2015-05-15 words: 5925 flesch: 87 summary: l′1 − bi )bi)k−1 i=1 , ( 2 + l′1 )|E(Lk−1)|) where l∗∗1 = k−1∑ i=1 ai. Then we have π′k−1 = ((k−1∑ i=1 (ai + bi) −a1 )a1 , · · · , (k−1∑ i=1 (ai + bi) −ak−1 )ak−1 , (k−1∑ i=1 (ai + bi) − b1 )b1 , · · · , (k−1∑ i=1 (ai + bi) − bk−1 )bk−1 , 2 (k−12 )∑ i,j,i6=j aiaj ) . keywords: graphic; i=1; sequence; | + cache: jacodesmath-15.pdf plain text: jacodesmath-15.txt item: #40 of 150 id: jacodesmath-155 author: V. Rajasekharaiah, Girish; Murthy, Usha P. title: Hyper-Zagreb indices of graphs and its applications date: 2021-01-24 words: 3433 flesch: 73 summary: [33] B. Zhou, I. Gutman, Further properties of Zagreb indices, MATCH Commun. [7] A. A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: Theory and applications, Acta Appl. keywords: graph; index; indices; vj)(ur cache: jacodesmath-155.pdf plain text: jacodesmath-155.txt item: #41 of 150 id: jacodesmath-156 author: Tomas Vetrik title: General degree distance of graphs date: 2021-05-16 words: 5589 flesch: 88 summary: So u1 is adjacent to n1 −1 pendant vertices, say v1,v2, . . . 2010 MSC: 05C35, 05C12, 92E10 Keywords: Degree distance, Chromatic number, Vertex connectivity 1. keywords: dda cache: jacodesmath-156.pdf plain text: jacodesmath-156.txt item: #42 of 150 id: jacodesmath-157 author: Kumari, Priyanka ; Keskar, Pradipkumar H. title: Algebraic methods in difference sets and bent functions date: 2021-05-20 words: 5959 flesch: 89 summary: ∈ Fm2 . ∈ Fm2 , π−1(a + L) −π−1(a) = {(l(xs+1, . . . keywords: difference cache: jacodesmath-157.pdf plain text: jacodesmath-157.txt item: #43 of 150 id: jacodesmath-158 author: Mittal, Gaurav ; Sharma, Rajendra title: On unit group of finite semisimple group algebras of non-metabelian groups of order 108 date: 2021-05-11 words: 5744 flesch: 84 summary: 20 October 2020 Journal of Algebra Combinatorics Discrete Structures and Applications On unit group of finite semisimple group algebras of non-metabelian groups of order 108 Research Article Gaurav Mittal, Rajendra. [12] G. Mittal, R. K. Sharma, On unit group of finite group algebras of non-metabelian groups up to order 72, Math Bohemica (2021) keywords: group; mnr; r=1; theorem cache: jacodesmath-158.pdf plain text: jacodesmath-158.txt item: #44 of 150 id: jacodesmath-159 author: Krebs, Mike title: Finite ε-unit distance graphs date: 2021-09-26 words: 3669 flesch: 79 summary: 3. Finite �-unit distance graphs with chromatic number ≥ 5 Carefully reading the proof of Theorem 2.2, we see that we do not require the full power of the point p being in the boundary of W . [2] G. Exoo, �-unit distance graphs, Discrete Comput. keywords: number; vertices cache: jacodesmath-159.pdf plain text: jacodesmath-159.txt item: #45 of 150 id: jacodesmath-160 author: Charan Barman, Sambhu; Amita Samanta Adhya; Sukumar Mondal; Jonecis Dayap title: Computation of minimum d-hop connected dominating set of trees in O(n) time date: 2022-07-09 words: 9000 flesch: 80 summary: A tree is called central tree if it has single central vertex and bi-central tree if it has two central vertices. Organization of our paper Section 2 describes the formation of BFS-tree T ′(u) and T(v) of tree T . keywords: dhd; domination; set; step; t(v; tree; vertex; weight cache: jacodesmath-160.pdf plain text: jacodesmath-160.txt item: #46 of 150 id: jacodesmath-162 author: Choosuwan, Parinyawat; Jitman, Somphong title: Self-dual codes over F_q+uF_q+u^2 F_q and applications date: 2020-09-06 words: 10641 flesch: 82 summary: 4. Self-dual quasi-abelian codes over principal ideal group alge- bras In this section, the study of quasi-abelian codes over principal ideal group algebras is given. In the special case where the field characteristic is 3 and the Sylow 3-subgroup of the underlying finite abelian group has order 3, complete characterization and enumeration of quasi-abelian codes and self-dual quasi- abelian codes are presented in terms linear codes and self-dual linear codes over F3m + keywords: abelian; codes; dual; fpm; hermitian; length; length n; linear; self; u2fq; ufq cache: jacodesmath-162.pdf plain text: jacodesmath-162.txt item: #47 of 150 id: jacodesmath-163 author: Daskalov, Rumen; Metodieva, Elena title: Generating generalized necklaces and new quasi-cyclic codes date: 2020-09-06 words: 3922 flesch: 78 summary: These two databases are updated when new codes are discovered. [2] N. Aydin, I. Siap, New quasi–cyclic codes over F5, Appl. keywords: algebra; codes; linear; necklaces; quasi cache: jacodesmath-163.pdf plain text: jacodesmath-163.txt item: #48 of 150 id: jacodesmath-164 author: Kumar, Pankaj; Devi, Pinki title: Minimum distance and idempotent generators of minimal cyclic codes of length ${p_1}^{\alpha_1}{p_2}^{\alpha_2}{p_3}^{\alpha_3}$ date: 2021-09-26 words: 12715 flesch: 92 summary: Hence C p α1 1 (q v1 ) a1 ×C p α2 2 (q v2 ) a2 ×C p α3 3 (q v3 ) a3 ⊂{(a1,a2,a3),(a1q,a2q,a3q), . . . 167–195 Similarly, we get C p α1 1 (q v1 ) a1q ×C p α2 2 (q v2 ) a2q ×C p α3 3 (q v3 ) a3q ⊂{(a1,a2,a3),(a1q,a2q,a3q), . . . keywords: c p; p α1; p α2; p α3; p β2; p β3 cache: jacodesmath-164.pdf plain text: jacodesmath-164.txt item: #49 of 150 id: jacodesmath-166 author: Sharma, Sunny Kumar; Kumar Bhat, Vijay title: On metric dimension of plane graphs $\mathfrak{J}_{n}$, $\mathfrak{K}_{n}$ and $\mathfrak{L}_{n}$ date: 2021-09-26 words: 9542 flesch: 88 summary: = γ(a1|{p1, t1}); and for 2 ≤ h ≤ w + 1, we have γ(t1|{p1, th}) = γ(r2|{p1, th}), a contradiction. {q1,ah}, ah (1 ≤ h ≤ n) = { (2l, 2w − 2l + 3, 2l− 2), 2 ≤ l ≤ w (4w − 2l + 3, 2l− 2w, 4w − 2l + 2), w + 1 ≤ l ≤ 2w. keywords: 4w −; graph; vertices; − 2l; ≤ 2w; ≤ l; ≤ n; ≤ w cache: jacodesmath-166.pdf plain text: jacodesmath-166.txt item: #50 of 150 id: jacodesmath-167 author: Visweswaran, Subramanian; Premkumar T. Lalchandani title: The exact annihilating-ideal graph of a commutative ring date: 2021-05-16 words: 16804 flesch: 93 summary: I and so, Z(R) = I. (2) ⇒ (1) We claim that for any non-zero ideal J of R with J ⊆ I, Ann(J) = I. Let r ∈ Ann(J). We claim that r ∈ Rpn−i. keywords: eag(r; graph; ideal; ring cache: jacodesmath-167.pdf plain text: jacodesmath-167.txt item: #51 of 150 id: jacodesmath-17 author: Linton, Steve; Niemeyer, Alice C.; Praeger, Cheryl E. title: Identifying long cycles in finite alternating and symmetric groups acting on subsets date: 2015-05-15 words: 16668 flesch: 85 summary: By assumption, v ≤ n − k − 1 and so u = n−v ≥ k + 1 and k0 ≤ min{k,u} = k. Also ck0 (γ ∩ Σ(g),g) divides ck(γ,g), and hence divides rm. ≤ k0 ≤ k. Let g ∈N and let C be the m-cycle contained in g. keywords: cycle; lemma; n k cache: jacodesmath-17.pdf plain text: jacodesmath-17.txt item: #52 of 150 id: jacodesmath-170 author: Kim, Jon-Lark; Ohk, Dong Eun; Park, Doo Young; Park, Jae Woo title: Recent results on Choi's orthogonal Latin squares date: 2022-01-13 words: 5568 flesch: 78 summary: In particular, orthogonal Latin squares have been one of the main topics in Latin squares. He introduced a pair of orthogonal Latin squares of order 9 in his book. keywords: aij; choi; latin; order; squares cache: jacodesmath-170.pdf plain text: jacodesmath-170.txt item: #53 of 150 id: jacodesmath-172 author: Epstein, Michael title: The covering numbers of the McLaughlin group and some primitive groups of low degree date: 2022-07-09 words: 5290 flesch: 69 summary: As we only consider covers consisting of maximal subgroups, we must include every member of U. Consequently, we need no longer consider the conjugacy classes of subgroups in U, nor the conjugacy classes of principal subgroups covered by the members of U. First, that one need only consider covers consisting of maximal subgroups, and second, that in order to prove that a collection C of proper subgroups is a cover of a group G it is sufficient to show that each of the maximal cyclic subgroups is contained in a subgroup from C. We call the maximal cyclic subgroups of G the principal subgroups of G and a generator of a principal subgroup is called a principal element of G. In light of these observations, the first step in determining the covering number of a group G is to determine the maximal subgroups and principal subgroups of G up to conjugacy. keywords: class; classes; conjugacy; cover; covering; number; subgroups cache: jacodesmath-172.pdf plain text: jacodesmath-172.txt item: #54 of 150 id: jacodesmath-176 author: Alhevaz, Abdollah; Baghipur, Maryam; Hashemi, Ebrahim; Shang, Yilun title: Some upper and lower bounds for $D_{\alpha}$-energy of graphs date: 2023-04-10 words: 5855 flesch: 84 summary: √∑n i=1 Tr 2 i n + (1 −α) √∑n i=1 Tr 2 i n + √ (n− 2) ( 2ζ − (1 −α)2 ∑n i=1 Tr 2 i n − (1 −α)2 ∑n i=1 Tr 2 i n2 ) . Consequently, EDα(G) ≤ (1 −α) √∑n i=1 Tr 2 i n + (1 −α) √∑n i=1 Tr 2 i n + √ (n− 2) ( 2ζ − (1 −α)2 ∑n i=1 Tr 2 i n − (1 −α)2 ∑n i=1 Tr 2 i n2 ) . keywords: 2αw(g)n; distance; graph; i=1 cache: jacodesmath-176.pdf plain text: jacodesmath-176.txt item: #55 of 150 id: jacodesmath-177 author: Hasan, Ayazul title: Subsocles and direct sum of uniserial modules: Subsocles and direct sum of uniserial modules date: 2021-09-26 words: 3622 flesch: 70 summary: 8(3) • 213–218 Received: 27 November 2020 Accepted: 16 April 2021 Journal of Algebra Combinatorics Discrete Structures and Applications Subsocles and direct sum of uniserial modules Research Article Ayazul Hasan Abstract: Suppose M is a QTAG-module with a subsocle S such that M/S is a direct sum of uniserial modules. A module M is called a serial module if it is a direct sum of uniserial modules. keywords: direct; modules; sum cache: jacodesmath-177.pdf plain text: jacodesmath-177.txt item: #56 of 150 id: jacodesmath-180 author: Gowthaman, Karthick ; Gupta, Somi; Mohan, Cruz; Guenda, Kenza; Chinnapillai, Durairajan title: Cyclic DNA codes over the ring $\mathbb{Z}_4+u\mathbb{Z}_4+u^2\mathbb{Z}_4$ date: 2021-09-26 words: 6538 flesch: 78 summary: 219–231 References [1] T. Abualrub, R. Oehmke, On the generators of Z4 cyclic codes of length 2e, IEEE Transactions on Information Theory 49 (2003) 2126–2133. [10] H. Q. Dinh, S. Pattanayak, A. K. Singh, S. Sriboonchitta, Construction of cyclic DNA codes over the ring Z4[u]/(u2 −1) based in deletion distance, Theoretical Computer Science 773 (2018) 27–42. keywords: 2(1; code; complement; cyclic; dna; length; p(x; q(x; reverse; ring cache: jacodesmath-180.pdf plain text: jacodesmath-180.txt item: #57 of 150 id: jacodesmath-185 author: Prakash, Om; Patel, Shikha title: A note on two-dimensional cyclic and constacyclic codes date: 2022-07-09 words: 5868 flesch: 83 summary: 9(3) • 161–174 Received: 11 January 2021 Accepted: 31 March 2022 Journal of Algebra Combinatorics Discrete Structures and Applications A note on two-dimensional cyclic and constacyclic codes Research Article Om Prakash, Shikha Patel Abstract: During the study of the two-dimensional cyclic (TDC) codes of length n = ls over a finite field Fq where s = 2k, Sepasdar and Khashyarmanesh (2016, [11]) arose a problem that the technique used by them to characterize TDC codes of length n = ls does not work for TDC codes of length 3l. In [11], Sepasdar and Khashyarmanesh studied the algebraic structure of TDC codes of length n = l2k over the finite field. keywords: codes; cyclic; fq[u]/〈ul; g(u; length; polynomials cache: jacodesmath-185.pdf plain text: jacodesmath-185.txt item: #58 of 150 id: jacodesmath-188 author: Kaliappan, Sowndhariya; Muthusamy, Appu title: Decomposition of cartesian product of complete graphs into sunlet graphs of order eight date: 2022-01-13 words: 18268 flesch: 70 summary: An L8- decomposition of K12�K10( x1i x 2 i x 3 i x 4 i x1k x 2 k x 3 k x 4 k ) , ( x5i x 6 i x 7 i x 8 i x5k x 6 k x 7 k x 8 k ) , ( x1i x 9 i x 2 i x 10 i x6i x 9 k x 5 i x 10 k ) for (i, k) = (1, 7), (2, 8), (3, 6), (4, 5), (5, 11), (6, 12), (7, 10), (8, 9), (9, 2), (10, 1), (11, 3), (12, 4);( x7i x 9 i x 8 i x 10 i x7k x 9 k x 8 k x 10 k ) for (i, k) = (1, 8), (2, 7), (3, 12), (4, 11), (5, 12), (6, 11); c ( x7i x 9 i x 8 i x 10 i x3i x 5 i x 6 i x 4 i ) for i = 7, ..., 12; ( x3i x 5 i x 4 i x 6 i x7i x 10 i x 2 i x 8 i ) for i = 1, ..., 6;( x3i x 5 i x 4 i x 6 i x3k x 5 k x 4 k x 6 k ) for (i, k) = (7, 2), (8, 1), (9, 11), (10, 12), (11, 6), (12, 5);( x j 1 x j 2 x j 3 x j 4 xk1 x k 2 x k 3 x k 4 ) for (j, k) = (1, 3), (3, 10), (4, 7), (5, 7), (6, 10), (7, 1)(8, 2), (9, 3), (10, 4);( x j 5 x j 6 x j 7 x j 8 xk5 x k 6 x k 7 x k 8 ) for (j, k) = (1, 3), (3, 7), (4, 7), (5, 7), (6, 8), (7, 1)(8, 2), (9, 3);( x j 9 x j 10 x j 11 x j 12 xk9 x k 10 x k 11 x k 12 ) for (j, k) = (1, 3), (2, 4), (3, 7), (4, 7), (5, 7), (6, 8), (7, 1)(8, 2), (9, 3), (10, 5);( x j 1 x j 5 x j 2 x j 6 xi3 x k 5 x i 4 x k 6 ) for (j, k) = (3, 8), (4, 8), (5, 9), (6, 9);( x j 1 x j 5 x j 2 x j 6 xk1 x k 5 x k 2 x k 6 ) for (j, k) = (1, 5), (2, 6), (7, 2), (8, 1), (9, 4), (10, 9);( x j 3 x j 9 x j 4 x j 10 xk3 x k 9 x k 4 x k 10 ) for (j, k) = (2, 6), (3, 8), (4, 8), (6, 9), (7, 2), (8, 1), (9, 4), (10, 9);( x j 7 x j 11 x j 8 x j 12 xk7 x k 11 x k 8 x k 12 ) for (j, k) = (2, 6), (3, 8), (4, 8), (5, 1), (6, 9), (7, 2), (8, 1), (9, 4), (10, 9);( x j 1 x j 11 x j 2 x j 12 x j 3 x j 9 x j 4 x j 10 ) for i = 2, 7, 8, 9, 10;( x j 1 x j 11 x j 2 x j 12 xk1 x j 4 x k 2 x j 3 ) for (j, k) = (3, 9), (4, 8), (5, 9), (6, 9);( x j 5 x j 9 x j 6 x j 10 x j 7 x j 1 x j 8 x j 2 ) , ( x j 3 x j 7 x j 4 x j 8 x j 5 x j 9 x j 6 x j 10 ) , for j = 1, ..., 10;( x21 x 2 2 x 2 3 x 2 4 x28 x 2 7 x 2 12 x 2 11 ) , ( x25 x 2 6 x 2 7 x 2 8 x212 x 2 11 x 4 7 x 4 8 ) , ( x105 x 10 6 x 10 7 x 10 8 x45 x 4 6 x 4 7 x 4 8 ) , ( x13 x 1 9 x 1 4 x 1 10 x53 x 1 11 x 5 4 x 1 12 ) ,( x53 x 5 9 x 5 4 x 5 10 x93 x 1 9 x 9 4 x 1 10 ) , ( x17 x 1 11 x 1 8 x 1 12 x12 x 1 4 x 1 1 x 1 3 ) , ( x11 x 1 11 x 1 2 x 1 12 x13 x 1 6 x 1 4 x 1 5 ) . An L8- decomposition of K13�K5( x j 5 x j 9 x j 6 x j 10 x j 3 x 3 9 x j 4 x 3 10 ) , ( x j 3 x j 12 x j 4 x j 13 x j 11 x j 2 x j 9 x j 7 ) for j = 2, 4;( x j 7 x j 8 x j 10 x j 11 x j 9 x j 2 x j 1 x j 13 ) for j = 1, 5; ( x j 1 x j 13 x j 8 x j 12 x j 7 x 3 13 x j 9 x 3 12 ) for j = 2, 5;( x j 9 x j 12 x j 10 x j 13 x j 8 x j 6 x j 4 x j 5 ) for j = 3, 4; ( x1i x 2 i x 4 i x 3 i x1k x 2 k x 4 k x 3 k ) for (i, k) = (5, 7), (8, 11);( x j 1 x j 5 x j 2 x j 6 x j k1 x k2 5 x k2 2 x k2 6 ) for (j, k1, k2) = (1, 9, 4), (2, 8, 5), (3, 9, 2);( x1i x 2 i x 5 i x 4 i x1k1 x 2 k2 x5k1 x 4 k2 ) for (i, k1, k2) = (9, 10, 11), (10, 2, 1), (13, 6, 6);( x41 x 4 5 x 4 2 x 4 6 x51 x 5 5 x 4 11 x 5 6 ) , ( x51 x 5 5 x 5 2 x 5 6 x31 x 3 5 x 3 2 x 3 6 ) , ( x13 x 1 7 x 1 4 x 1 8 x33 x 5 7 x 3 4 x 4 8 ) , ( x23 x 2 7 x 2 4 x 2 8 x21 x 4 7 x 3 4 x 5 8 ) ,( x33 x 3 7 x 3 4 x 3 8 x39 x 3 1 x 3 2 x 2 8 ) , ( x43 x 4 7 x 4 4 x 4 8 x23 x 3 7 x 3 4 x 5 8 ) , ( x53 x 5 7 x 5 4 x 5 8 x33 x 5 5 x 5 11 x 3 8 ) , ( x15 x 1 9 x 1 6 x 1 10 x55 x 3 9 x 1 12 x 3 10 ) ,( x35 x 3 9 x 3 6 x 3 10 x33 x 3 7 x 3 4 x 3 1 ) , ( x55 x 5 9 x 5 6 x 5 10 x513 x 3 9 x 1 6 x 3 10 ) , ( x11 x 1 4 x 1 5 x 1 11 x12 x 1 6 x 1 8 x 3 11 ) , ( x21 x 2 4 x 2 5 x 2 11 x22 x 4 4 x 2 8 x 5 11 ) ,( x31 x 3 4 x 3 5 x 3 11 x41 x 3 13 x 3 8 x 3 6 ) , ( x41 x 4 4 x 4 5 x 4 11 x42 x 4 3 x 4 8 x 1 11 ) , ( x51 x 5 4 x 5 5 x 5 11 x52 x 5 6 x 5 8 x 5 3 ) , ( x12 x 1 3 x 1 6 x 1 7 x111 x 1 4 x 1 5 x 1 13 ) ,( x22 x 2 3 x 2 6 x 2 7 x211 x 2 4 x 2 5 x 2 10 ) , ( x32 x 3 3 x 3 6 x 3 7 x311 x 2 3 x 3 5 x 3 10 ) , ( x42 x 4 3 x 4 6 x 4 7 x49 x 4 1 x 4 5 x 4 10 ) , ( x52 x 5 3 x 5 6 x 5 7 x511 x 5 4 x 5 5 x 3 7 ) , 44 K. Sowndhariya, A. Muthusamy / J. Algebra Comb. keywords: decomposition; j =; j k; mod; x j; x k; x11 x; x3i x cache: jacodesmath-188.pdf plain text: jacodesmath-188.txt item: #59 of 150 id: jacodesmath-19 author: Yanling, Fengnan; Wang, Zhao; Ye, Chengfu; Zhang, Shumin title: The rainbow vertex-index of complementary graphs date: 2015-09-15 words: 2896 flesch: 82 summary: So, we give G a vertex-coloring as follows: color vertex x with 1 and color all vertices of N3G(x) with 2. For a graph G, let V (G), E(G), n(G), m(G), and G, respectively, be the set of vertices, the set of edges, the order, the size, and the complement graph of G. ∗ Supported by the National Science Foundation of China (No. 11161037, 11101232, 11461054) and the Science Found of Qinghai Province (No. 2014-ZJ-907). keywords: rainbow; vertex cache: jacodesmath-19.pdf plain text: jacodesmath-19.txt item: #60 of 150 id: jacodesmath-194 author: Barrientos, Christian title: On the generation of alpha graphs date: 2022-04-30 words: 8344 flesch: 80 summary: Introduction The roots of difference vertex labelings can be found in the area of combinatorial design, in particular, this type of graph labeling was introduced as a mechanism to determine the veracity of two conjectures associated with the decomposition of complete graphs into copies of a given tree. 101–114 there exists a ρ-labeling of G. Therefore, in these three articles we can see the origin of the most famous conjecture in the area of graph labeling, known as the graceful tree conjecture that expresses that every tree admits a graceful labeling. keywords: graph; labeling; set; vertex; vertices cache: jacodesmath-194.pdf plain text: jacodesmath-194.txt item: #61 of 150 id: jacodesmath-195 author: Beasley, LeRoy; Santana, Manuel A. ; Mousley, Jonathan ; Brown, David E title: Cordiality of digraphs date: 2022-12-13 words: 7002 flesch: 85 summary: Let D ∈ Tn with vertex labelling f and induced arc labelling g. Let Λf,g(D) = (α,β,γ). Also there are k such vertices so there are k(k − 1)/2 arcs between pairs of vertices each labelled 0. keywords: arcs; labelling; set; vertices cache: jacodesmath-195.pdf plain text: jacodesmath-195.txt item: #62 of 150 id: jacodesmath-197 author: Vega, Gerardo title: Lee weight distributions of trace codes over F_q+uF_q from irreducible cyclic codes date: 2023-04-10 words: 5281 flesch: 74 summary: With this equivalence in mind, and by using the already known weight distributions of an infinite family of irreducible cyclic codes (semiprimitive and not semiprimitive), we follow the open problem suggested in the Conclusion of [11] to determine the Lee weight distribution of an infinite family of trace codes over the ring Fq + uFq, that includes the infinite family found in [11]. 2010 MSC: 94B15 · 11T71 Keywords: Codes over a ring, Trace codes, Semiprimitive codes and cyclotomic classes, Irreducible cyclic codes 1. The Lee weight distribution of an extended family of trace codes over Fq + uFq We are now going to follow the open problem suggested in the Conclusion of [11], and determine the Lee weight distribution of trace codes of the form CLe in terms of other class of irreducible cyclic codes, with known or well-understood weight distribution. keywords: codes; cyclic; irreducible; lee; trace; weight cache: jacodesmath-197.pdf plain text: jacodesmath-197.txt item: #63 of 150 id: jacodesmath-20 author: Yao, Ting; Shi, Minjia; Sole, Patrick title: Skew cyclic codes over $F_{q}+uF_{q}+vF_{q}+uvF_{q}$ date: 2015-09-15 words: 3191 flesch: 84 summary: Section 3 derives the structure of linear codes over R. In Section 4, we introduce skew cyclic codes over ring R and give the structural properties of skew cyclic codes over R through a decomposition theorem. First, we introduce the structure of linear codes over R and show the structural properties of skew cyclic codes over R. Next, we give the enumeration of distinct skew cyclic codes over R when n is odd. keywords: codes; cyclic; skew cache: jacodesmath-20.pdf plain text: jacodesmath-20.txt item: #64 of 150 id: jacodesmath-203 author: V. Rajasekharaiah, Girish ; P. Murthy, Usha; Subramanya, Umesh title: Protection of a network by complete secure domination date: 2022-01-13 words: 4908 flesch: 84 summary: If γcsd(G) < |D|, then there exits at least one vertex say vj ∈ V (G), (D −{vi})∪{vj},vi ∈ D is not a dominating set. If γcsd(G) < |D|, then there exits at least one vertex say vj ∈ V (G), (D −{vi})∪{vj},vi ∈ D is not a dominating set. keywords: dominating; set cache: jacodesmath-203.pdf plain text: jacodesmath-203.txt item: #65 of 150 id: jacodesmath-21 author: Khoshnoudirad, Daniel title: A further study for the upper bound of the cardinality of Farey vertices and application in discrete geometry date: 2015-09-15 words: 7069 flesch: 83 summary: The Farey sequence of order n is the set Fn = { 0 }⋃{p q , ∣∣∣1 ≤ p ≤ q ≤ n,p∧q = 1} . B ′ 2(m,n) ≤ n 2mn∑ q=1 q∑ p=1 p∧q=1 2mn∑ q′=1 q′∑ p′=1 p′∧q′=1 1 d′s′ ≤ n 2mn∑ d′=1 b2mn d′ c∑ s=1 b2mn d′s c∑ s′=1 d′s∑ r=1 d′s′∑ r′=1 ⌊ min( d ′s r , d ′s′ r′ ) ⌋∑ d=1 1 d′s′ ≤ n 2mn∑ d′=1 b2mn d′ c∑ s=1 b2mn d′s c∑ s′=1 d′s∑ r=1 d′s′∑ r′=1 1 r′ ≤ K′n 2mn∑ d′=1 b2mn d′ c∑ s=1 b2mn d′s c∑ s′=1 d′s ln(d′s′) + Kn3m2 ln2(mn) ≤ K′n ln(2mn) 2mn∑ d′=1 b2mn d′ c∑ s=1 d′s 2mn d′s + Kn3m2 ln2(mn) ≤ K′n2m ln(2mn) 2mn∑ d′=1 b2mn d′ c∑ s=1 1 + Kn3m2 ln2(mn) ≤ K′n2m ln(2mn) 2mn∑ d′=1 2mn d′ + Kn3m2 ln2(mn) ≤ K”n3m2 ln2(mn). keywords: b2mn; d′=1; d′s; farey; ln2(mn; n p′ cache: jacodesmath-21.pdf plain text: jacodesmath-21.txt item: #66 of 150 id: jacodesmath-211 author: Munuera Merayo, Diego title: On Mignotte secret sharing schemes over Gaussian integers date: 2022-07-09 words: 5404 flesch: 81 summary: Given two Gaussian Integers v,z ∈ Z[i] with z 6= 0, there exists q,r ∈ Z[i] such that r ∈F(z) and v = zq + r. Moreover such q and r are unique and N(r) ≤ N(z)/2. Proof. Thus, given v,z ∈ Z[i], the expression v (mod z) does not uniquely identify one element of Z[i]. keywords: gaussian; integers; mod; secret; z[i cache: jacodesmath-211.pdf plain text: jacodesmath-211.txt item: #67 of 150 id: jacodesmath-214 author: Ghajari, Arazgol ; Khashyarmanesh, Kazem ; Rajabi, Zohreh title: 1-generator two-dimensional quasi-cyclic codes over Z_4[u]/(u^2-1) date: 2022-01-13 words: 6662 flesch: 91 summary: QC codes form an important class of linear codes which also include cyclic codes (when we consider the case ` = 1). This method probably helps to decode two-dimensional cyclic codes and two-dimensional QC codes as it has done for cyclic codes and QC codes. keywords: codes; cyclic; generator; polynomials cache: jacodesmath-214.pdf plain text: jacodesmath-214.txt item: #68 of 150 id: jacodesmath-217 author: Aydin, Noah; Liu, Peihan; Yoshino, Bryan title: A database of quantum codes date: 2022-07-19 words: 3566 flesch: 79 summary: One of the search methods we consider in this paper is about deriving quantum codes from polycyclic codes associated with trinomials, which is based on the CSS construction. In section 2, we recall some basic concepts about quantum codes and polycyclic codes. keywords: codes; new; polycyclic; quantum; quantum codes cache: jacodesmath-217.pdf plain text: jacodesmath-217.txt item: #69 of 150 id: jacodesmath-218 author: Wilfong, Andrew title: Toric code distances from terraced polytopes date: 2022-12-13 words: 10644 flesch: 84 summary: In general, if [0,a] is considered as a subset of Rn for some n ∈ N, then d ([0,a]) = (q − 1)n−1 (q − 1 −a). ,q − 2, let Pi be the projection of the ith fiber P ∩π−1k keywords: distance; polytopes; q −; toric cache: jacodesmath-218.pdf plain text: jacodesmath-218.txt item: #70 of 150 id: jacodesmath-22 author: Louchard, Guy; Prodinger, Helmut title: Approximate counting with m counters: A probabilistic analysis date: 2015-09-15 words: 6849 flesch: 85 summary: − (l + j − − (l + j − keywords: 6=0; approximate; counters; counting; log; moments cache: jacodesmath-22.pdf plain text: jacodesmath-22.txt item: #71 of 150 id: jacodesmath-224 author: Mallik, Sudipta title: A new formula for the minimum distance of an expander code date: 2022-04-29 words: 2501 flesch: 82 summary: Sipser and Spielman constructed expander codes from bipartite expander graphs in [6]. The bi-adjacency matrix of the (5,4,2, 1 2 , 2 3 ) expander graph G in Figure 1 is given by B =   1 0 0 1 1 0 1 0 0 0 keywords: expander; graph; von(s cache: jacodesmath-224.pdf plain text: jacodesmath-224.txt item: #72 of 150 id: jacodesmath-225 author: Sarvate, Dinesh G.; Woldemariam, Dinkayehu M. title: A note on GDD(1, n, n, 4; λ_1, λ_2) date: 2022-04-30 words: 7595 flesch: 86 summary: For n = 3, λ1 ≡ λ2 (mod 3). A necessary condition for the existence of a GDD(1,2,2,4;λ1,λ2) is λ1 = λ2. keywords: gdd(1,n; mod cache: jacodesmath-225.pdf plain text: jacodesmath-225.txt item: #73 of 150 id: jacodesmath-226 author: Daniel Schwab, Emil title: The bicyclic semigroup as the quotient inverse semigroup by any gauge inverse submonoid date: 2022-05-13 words: 4196 flesch: 80 summary: Since ≤N is a preorder on the set S then it defines an equivalence relation 'N on S by s 'N t ⇔ s ≤N t and t ≤N s, and a partial order on the set of equivalence classes S/ 'N. Gauge inverse submonoids Following [5], a nontrivial right cancellative monoid M is a RILL monoid if 1M is indecomposable and any two elements s,t ∈ M that admit a common left multiple admit a least common left multiple s ∨ t. keywords: inverse; t)]gm cache: jacodesmath-226.pdf plain text: jacodesmath-226.txt item: #74 of 150 id: jacodesmath-23 author: Daskalov, Rumen; Hristov, Plamen title: Some new quasi-twisted ternary linear codes date: 2015-09-15 words: 2410 flesch: 82 summary: The problem of finding the parameters of the optimal codes is very difficult one (see [15], [9]) and has two aspects - one is the construction of new codes with better minimum distances and the other is to prove the nonexistence of codes with given parameters. These two databases are updated when new codes are discovered. keywords: code; linear cache: jacodesmath-23.pdf plain text: jacodesmath-23.txt item: #75 of 150 id: jacodesmath-233 author: Balogh, Zsolt Adam title: On the isomorphism of unitary subgroups of noncommutative group algebras date: 2022-04-30 words: 4582 flesch: 85 summary: Moreover, 0 = δ2 + δ3 = (α0 + α1 + α2 + 117 Z. A. Balogh / J. Algebra Comb. [Self-dual normal bases and unitary groups of characteristic 2], Transform. keywords: algebra; group cache: jacodesmath-233.pdf plain text: jacodesmath-233.txt item: #76 of 150 id: jacodesmath-234 author: Chen, Eric ; Jönsson, Fredrik title: New good quasi-cyclic codes and codes with improved minimum distance date: 2022-12-13 words: 3964 flesch: 90 summary: [15] R. Daskalov, E. Metodieva, Generating generalized necklaces and new quasi-cyclic codes, J. Algebra Comb. Computer search for quasi-cyclic codes A linear keywords: codes; cyclic; new; polynomials; quasi cache: jacodesmath-234.pdf plain text: jacodesmath-234.txt item: #77 of 150 id: jacodesmath-24 author: Maheshwari, Swati; Sharma, R. K. title: The unit group of group algebra $F_qSL(2;Z_3)$ date: 2016-01-15 words: 1952 flesch: 78 summary: 2010 MSC: 16U60, 20C05 Keywords: Group algebra, Unit group, Finite field 1. Unit group of algebra of circulant matrix has been discussed in [11, 17]. keywords: algebra; group; mod cache: jacodesmath-24.pdf plain text: jacodesmath-24.txt item: #78 of 150 id: jacodesmath-240 author: MOULOUA, El Mahdi; Najmeddine, M. title: On the parameters of a class of narrow sense primitive BCH codes date: 2023-08-17 words: 6059 flesch: 89 summary: With the same argument we have δ 3 = (q − 1)q m−1 − 1 −q m+1 2 = q m − 1 −q m−1 −q s+1 = (q − 2)q m−1 + (q − 1)q m−2 + · · · + (q − 1)q s+2 + (q − 2)q s+1 + (q − 1)q s + (q − 1)q s−1 + · · · + (q − 1)q + (q − 1). Indeed, we have K i = (q − 2)q m−1 + (q − 1)q m−2 + · · · + (q − 1)q s+2 + (q − 2)q s+1 + (q − 1)q s + (q − 1)q s−1 + · · · + (q − 1)q − keywords: 1)q; m−1; q − cache: jacodesmath-240.pdf plain text: jacodesmath-240.txt item: #79 of 150 id: jacodesmath-245 author: Tamilselvi, Annamalai; Shajahan, Dhilshath title: Walled Klein-4 Brauer algebras date: 2022-12-13 words: 7618 flesch: 83 summary: Walled Klein-4 Brauer algebras are iterated inflations We show that walled Klein-4 Brauer algebras are iterated inflations Multiplication of walled Klein-4 Brauer diagrams To find the product of two signed diagrams −→−→ d 1 and −→−→ d 2, draw −→−→ d 2 below −→−→ d 1 and connect the ith upper vertex of −→−→ d 2 with the ith lower vertex of −→−→ d 1. keywords: algebra; brauer; walled; ×z2; −→−→; −→−→q cache: jacodesmath-245.pdf plain text: jacodesmath-245.txt item: #80 of 150 id: jacodesmath-26 author: Morris, Dave Witte title: Infinitely many nonsolvable groups whose Cayley graphs are hamiltonian date: 2016-01-15 words: 11118 flesch: 80 summary: [4] D. Witte, J. A. Gallian, A survey: Hamiltonian cycles in Cayley graphs, Discrete Math. 51(3) (1984) 293–304. 30 http://amc-journal.eu/index.php/amc/article/view/177/147 http://amc-journal.eu/index.php/amc/article/view/177/147 http://arxiv.org/src/1009.5795/anc/A5.pdf http://arxiv.org/src/1009.5795/anc/A5.pdf http://www.sciencedirect.com/science/article/pii/0012365X84900104 http://www.sciencedirect.com/science/article/pii/0012365X84900104 Introduction Preliminaries Proof of Proposition 1.2 Details of hamiltonian cycles in A5 References 2010 MSC: 05C25, 05C45 Keywords: Cayley graph, Hamiltonian cycle, Solvable group, Alternating group 1. keywords: b −1 cache: jacodesmath-26.pdf plain text: jacodesmath-26.txt item: #81 of 150 id: jacodesmath-28 author: Schnyder, Reto; López-Ramos, Juan Antonio; Rosenthal, Joachim; Schipani, Davide title: An active attack on a multiparty key exchange protocol date: 2016-01-15 words: 2880 flesch: 76 summary: [4] M. Steiner, G. Tsudik, M. Waidner, Key agreement in dynamic peer groups, IEEE Trans. Furthermore, all users remember the same consistent values for key refreshment. keywords: attack; cn−1; key; users cache: jacodesmath-28.pdf plain text: jacodesmath-28.txt item: #82 of 150 id: jacodesmath-29 author: Seneviratne, Pani title: Generalized hypercube graph $\Q_n(S)$, graph products and self-orthogonal codes date: 2016-01-15 words: 5000 flesch: 88 summary: We study graph boolean products G1 = Qn(S) ×Q1, G2 = Qn(S) ∧Q1, G3 = Qn(S)[Q1] and show that binary codes from neighborhood designs of G1, G2 and G3 are self-orthogonal for all choices of n and S. More over, we show that the class of codes C1 are self-dual. In this Section we determine the binary codes C1,C2 and C3 from the neighborhood designs of graph products G1 = Qn(S) ×Q1, G2 = Qn(S) ∧Q1 and G3 = Qn(S)[Q1] respectively. keywords: graph; matrix; qn(s; set cache: jacodesmath-29.pdf plain text: jacodesmath-29.txt item: #83 of 150 id: jacodesmath-3 author: Tonchev, Vladimir D. title: The existence of optimal quaternary [28,20,6] and quantum [[28,12,6]] codes date: 2014-09-15 words: 1962 flesch: 78 summary: An extended version of Calderbank-Rains-Shor-Sloane table for quantum codes [2, Table III], as well as tables with bounds on the minimum distance of linear codes, was compiled by Grassl Using the connection to quantum codes described in Theorem 1.1, Lemma 2.1 implies the following. keywords: code; quantum; self cache: jacodesmath-3.pdf plain text: jacodesmath-3.txt item: #84 of 150 id: jacodesmath-31 author: Imran, Muhammad; Haq Bokhary, Syed Ahtsham Ul ; Baig, A. Q. title: On the metric dimension of rotationally-symmetric convex polytopes date: 2016-05-15 words: 9722 flesch: 89 summary: i = 2; (i, i− 2, k − i + 1), 3 ≤ i ≤ k; (k, k − 1, 1), i = k + 1; (k − 1, k, 2), i = k + 2; (2k − i + 1, 2k − i + 3, i−k), k + 3 ≤ i ≤ 2k. ≤ k keywords: cycle; k +; resolving; vertex; ≤ t cache: jacodesmath-31.pdf plain text: jacodesmath-31.txt item: #85 of 150 id: jacodesmath-32 author: Francis, Amanda E.; Humphries, Stephen P. title: Commutative Schur rings over symmetric groups II: The case n = 6 date: 2016-05-15 words: 11732 flesch: 87 summary: If C ⊆ G satisfies C ∈ S and ∑ g∈G λgg ∈ S, then for all λ Assume first that C−1 = C. Then we can write C = ∑72 i=1 xi(αi keywords: case; conjugate; principal; ring; set cache: jacodesmath-32.pdf plain text: jacodesmath-32.txt item: #86 of 150 id: jacodesmath-33 author: Sorgun, Sezer; Topcu, Hatice title: On the spectral characterization of kite graphs date: 2016-05-15 words: 3463 flesch: 84 summary: 2010 MSC: 05C50, 05C75 Keywords: Kite graph, Cospectral graphs, Clique number, Determined by adjacency spectrum 1. Also, we prove that Kitep,2 graphs are determined by their adjacency spectrum. keywords: graph cache: jacodesmath-33.pdf plain text: jacodesmath-33.txt item: #87 of 150 id: jacodesmath-34 author: Hadjirezaei, Somayeh; Karimzadeh, Somayeh title: Matrix rings over a principal ideal domain in which elements are nil-clean date: 2016-05-15 words: 2649 flesch: 91 summary: References [1] S. Breaz, G. Călugăreanu, P. Danchev, T. Micu, Nil-clean matrix rings, Linear Algebra Appl. 439(10) (2013) 3115-3119. For r ∈ R, it is easily seen that rY X = 0 if and only if r = 0. keywords: matrix; ring cache: jacodesmath-34.pdf plain text: jacodesmath-34.txt item: #88 of 150 id: jacodesmath-36 author: Jeyanthi, Pon; Maheswar, Anthony; Vijayalakshm, Mani title: New results on vertex equitable labeling date: 2016-05-15 words: 4432 flesch: 91 summary: [ Pm; C 2 n ] , ⟨Pm◦̂K1,n⟩, kC4-snakes for all k ≥ 1, generalized kCn-snakes if n ≡ 0 (mod 4), n ≥ 4 and the graphs obtained by duplicating an arbitrary vertex and an arbitrary edge of a cycle Cn, total graph of Pn, splitting graph of Pn and fusion of two edges of a cycle Cn are vertex equitable graphs. In this paper, we prove that S(D(Tn)), S(D(Qn)), S(DA(Tn)), S(DA(Qn)), DA(Qm) ⊙ nK1 and DA(Tm) ⊙ nK1 are vertex equitable graphs. keywords: b b; labeling; vertex cache: jacodesmath-36.pdf plain text: jacodesmath-36.txt item: #89 of 150 id: jacodesmath-37 author: Khoshnoudirad, Daniel title: Erratum to “A further study for the upper bound of the cardinality of Farey vertices and applications in discrete geometry” [J. Algebra Comb. Discrete Appl. 2(3) (2015) 169-190] date: 2016-05-15 words: 5928 flesch: 83 summary: The Farey sequence of order n is the set Fn = { 0 }⋃{p q , ∣∣∣1 ≤ p ≤ q ≤ n,p∧q = 1} We mention [14] as a forthcoming modern reference work on the Farey sequences. ≤ k ≤ n q′ (because of the preliminary.) 111 D. Khoshnoudirad / J. Algebra Comb. keywords: b2mn; farey; order cache: jacodesmath-37.pdf plain text: jacodesmath-37.txt item: #90 of 150 id: jacodesmath-39 author: Tonchev, Vladimir D. title: Editor’s note date: 2016-09-15 words: 256 flesch: 27 summary: The current Special Issue contains papers on covering arrays and their applications, group divisible designs, automorphism groups of combinatorial designs, covering number of permutation groups, tourna- ments, large sets of geometric designs, partitions, quasi-symmetric functions, resolvable Steiner systems, and weak isometries of Hamming spaces. Received: 11 April 2016 Journal of Algebra Combinatorics Discrete Structures and Applications Editor’s note Vladimir D. Tonchev This Special Issue, entitled Algebraic Combinatorics and Applications, of the Journal of Algebra, Combinatorics, Discrete Structures, and Applications, contains selected papers submitted by conference participants at the Algebraic Combinatorics and Applications: keywords: applications cache: jacodesmath-39.pdf plain text: jacodesmath-39.txt item: #91 of 150 id: jacodesmath-4 author: Oliver, Kamilla; Prodinger, Helmut title: Horizontal runs in domino tilings date: 2014-09-15 words: 2347 flesch: 77 summary: 1/α + εh and continue 1 − 1 α −εh − 1 α2 − 2εh α + α−2h−1 ∼ 0, or εh ∼ √ 5α−2h−1. 21 Horizontal runs in domino tilings We write 1 −z −z2 + z2h+1 ∼ ( 1 − z ρh ) C, and find C = lim z→ρh 1 −z −z2 + z2h+1 1 − z ρh ∼ √ 5 α . − 4z2 + z4 + 4z2h+2 − 2z4h+2 . keywords: −z2 cache: jacodesmath-4.pdf plain text: jacodesmath-4.txt item: #92 of 150 id: jacodesmath-40 author: Colbourn, Charles J.; Fan, Bingli title: Locating one pairwise interaction: Three recursive constructions date: 2016-09-15 words: 4078 flesch: 80 summary: While well studied, covering arrays do not enable one to determine the specific levels of factors causing the faults; locating arrays ensure that the results from test suite execution suffice to determine the precise levels and factors causing faults, when the number of such causes is small. 2010 MSC: 05B30, 05A18, 05D99, 62K05, 68P10 Keywords: Locating array, Covering array, Detecting array 1. keywords: arrays cache: jacodesmath-40.pdf plain text: jacodesmath-40.txt item: #93 of 150 id: jacodesmath-41 author: Colbourn, Charles J.; Keranen, Melissa S.; Kreher, Donald L. title: The 3-GDDs of type $g^3u^2$ date: 2016-09-15 words: 6259 flesch: 93 summary: 3(3) • 135–144 Received: 23 October 2015 Accepted: 17 February 2016 Journal of Algebra Combinatorics Discrete Structures and Applications The 3-GDDs of type g3u2 Research Article Charles J. Colbourn, Melissa S. Keranen, Donald L. Kreher Abstract: A 3-gdd of type g3u2 exists if and only if g and u have the same parity, 3 divides u and u ≤ 3g. Such a 3-gdd of type g3u2 is equivalent to an edge decomposition of Kg,g,g,u,u into triangles. There exist 3-gdds of types 4362 and 1332 and a 3-igdd of type (5 : 1)3(9 : 3)2 from Lemma 3.7. keywords: exists; gdd; groups; igdd; mod; proof; theorem; type cache: jacodesmath-41.pdf plain text: jacodesmath-41.txt item: #94 of 150 id: jacodesmath-42 author: Crnković, Dean; Danilović, Doris Dumičić ; Rukavina, Sanja title: Enumeration of symmetric (45,12,3) designs with nontrivial automorphisms date: 2016-09-15 words: 5283 flesch: 74 summary: [5] V. Ćepulić, On symmetric block designs (45,12,3) with automorphisms of order 5, Ars Combin. [24] V. Mandekić-Botteri, On symmetric block designs (45,12,3) with involutory automorphism fixing 15 points, Glas. keywords: automorphism; codes; designs; graphs; group; symmetric cache: jacodesmath-42.pdf plain text: jacodesmath-42.txt item: #95 of 150 id: jacodesmath-43 author: Epstein, Michael; Magliveras, Spyros S. title: The covering number of $M_{24}$ date: 2016-09-15 words: 1809 flesch: 76 summary: [9] M. S. Lucido, On the covers of finite groups, in: C. M. Campbell, E. F. Robertson, G. C. Smith (Eds), Groups St. Andrews 2001, in Oxford, vol II, in : London Math. 2010 MSC: 20B40, 20D05, 20E07, 20E32 Keywords: Group theory, Group coverings, Finite simple groups 1. keywords: covering; group; subgroups cache: jacodesmath-43.pdf plain text: jacodesmath-43.txt item: #96 of 150 id: jacodesmath-44 author: Froncek, Dalibor; Shepanik, Aaron title: Regular handicap tournaments of high degree date: 2016-09-15 words: 3054 flesch: 70 summary: This, together with the result by Kovář [P. Kovář, On regular handicap graphs, personal communi- cation, June 16, 2016] and Kovářová [T. Kovářová, On regular handicap graphs, personal communication, June 16, 2016], gives an almost complete characterization of handicap graphs for n ≡ 2 (mod 4). [4] D. Froncek, Handicap distance antimagic graphs and incomplete tournaments, AKCE Int. keywords: distance; graph; handicap; labeling cache: jacodesmath-44.pdf plain text: jacodesmath-44.txt item: #97 of 150 id: jacodesmath-45 author: Hurley, Michael R.; Khadka, Bal K.; Magliveras, Spyros S. title: Some new large sets of geometric designs of type ${LS[3][2,3,2^8]}$ date: 2016-09-15 words: 7433 flesch: 76 summary: 2010 MSC: 05B25, 05B40, 05E18 Keywords: Geometric t-designs, Large sets of geometric t-designs, t-designs over GF(q), Parallelisms, Lattice basis reduction, LLL algorithm. In this article we deal with large sets of geometric t-designs. keywords: designs; orbits; sets cache: jacodesmath-45.pdf plain text: jacodesmath-45.txt item: #98 of 150 id: jacodesmath-46 author: Keith, William J. title: The part-frequency matrices of a partition date: 2016-09-15 words: 5121 flesch: 67 summary: Since the number of partitions of orbit size 1 is of interest in possible elementary proofs for partition congruences, what can be said – whether combinatorially, analytically or asymptotically – about its coefficients? Orbits of size 2 will will contain either a fixed point as in the orbits of size 1, or fillings of every other entry in an antidiagonal with the same entry. It seems interesting, and hopefully useful, that a map which is a small modification of Glaisher’s old bijection should have such close connections to the overarching structure of partition congruences now known to exist. keywords: mod; number; partitions; parts; size cache: jacodesmath-46.pdf plain text: jacodesmath-46.txt item: #99 of 150 id: jacodesmath-47 author: Mwesigwa, Ronald; Sarvate, Dinesh G.; Zhang, Li title: Group divisible designs of four groups and block size five with configuration (1; 1; 1; 2) date: 2016-09-15 words: 4919 flesch: 81 summary: [10] M. S. Keranen, M. R. Laffin, Fixed block configuration group divisible designs with block size six, Discrete Math. 308(4) (2012) 745–756. [4] H. L. Fu, C. A. Rodger, D. G. Sarvate, The existence of group divisible designs with first and second associates, having block size three, Ars Combin. 54 (2000) 33–50. keywords: block; groups; theorem cache: jacodesmath-47.pdf plain text: jacodesmath-47.txt item: #100 of 150 id: jacodesmath-48 author: Sun, Jie title: Quasisymmetric functions and Heisenberg doubles date: 2016-09-15 words: 3236 flesch: 66 summary: When An is the Hecke algebra at a generic value of q, the associated Heisenberg double is the usual Heisenberg algebra. [Quasisymmetric functions, noncommutative symmetric functions and Hecke algebras at q = 0], C. R. Acad. keywords: algebras; double; functions; heisenberg; tower cache: jacodesmath-48.pdf plain text: jacodesmath-48.txt item: #101 of 150 id: jacodesmath-49 author: Topalova, Svetlana title: On the resolutions of cyclic Steiner triple systems with small parameters date: 2016-09-15 words: 3330 flesch: 66 summary: That is why resolutions of cyclic designs are of particular interest and have been the subject of many papers. General constructions of resolutions of cyclic designs are presented in [7], [14], [17], [18]. keywords: automorphism; cyclic; designs; order; point; resolutions cache: jacodesmath-49.pdf plain text: jacodesmath-49.txt item: #102 of 150 id: jacodesmath-5 author: Kaya, Abidin; Yildiz, Bahattin title: New extremal binary self-dual codes of length 68 date: 2014-09-15 words: 5831 flesch: 85 summary: [2] S. T. Dougherty, T. A. Gulliver, M., Harada, Extremal binary self dual codes, IEEE Trans. 2010 MSC: 94B05, 94B60, 94B65 Keywords: Extremal codes, Codes over rings, Gray maps, Quadratic double-circulant codes 1. keywords: binary; codes; dual; self cache: jacodesmath-5.pdf plain text: jacodesmath-5.txt item: #103 of 150 id: jacodesmath-50 author: Bruner, Ryan; De Winter, Stefaan title: Weak isometries of Hamming spaces date: 2016-09-15 words: 4381 flesch: 81 summary: n. Two words of weight p have disjoint support if and only if there exists a unique word of weight 2p at distance p from both words. Proof. Now let φ be any permutation of the vertex set of Γ that maps vertices at distance p to vertices at distance p, for some specific 1 ≤ p ≤ d. keywords: distance; isometry cache: jacodesmath-50.pdf plain text: jacodesmath-50.txt item: #104 of 150 id: jacodesmath-51 author: Guo, Zhiwei; Zhao, Haixing; Mao, Yaping title: On the matching polynomial of hypergraphs date: 2016-01-15 words: 4109 flesch: 76 summary: 11 http://dx.doi.org/10.1016/j.dam.2010.01.002 http://dx.doi.org/10.1016/j.dam.2010.01.002 http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-94991 http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-94991 http://dx.doi.org/10.1007/s00373-016-1685-z http://dx.doi.org/10.1007/s00373-016-1685-z http://dx.doi.org/10.1016/0166-218X(88)90081-9 http://dx.doi.org/10.1016/0166-218X(88)90081-9 Introduction The fundamental theorem for matching polynomials Matching polynomials of some special hypergraphs Zeros of matching polynomials of a hypergraphs References Further, we discuss the zeros of matching polynomials of hypergraphs. keywords: hypergraph; let; matching; polynomial cache: jacodesmath-51.pdf plain text: jacodesmath-51.txt item: #105 of 150 id: jacodesmath-52 author: Chandoul, Amara title: On the norms of r-circulant matrices with generalized Fibonacci numbers date: 2017-01-15 words: 2456 flesch: 86 summary: You cannot go very far in the lore of Fibonacci numbers without encountering the companion sequence of Lucas numbers {Ln}∞n=0, which follows the same recursive pattern as the Fibonacci numbers, but begins with other initial values. 2010 MSC: 15B05, 15A60, 65F35 Keywords: Matrix norm, r-circulant matrices, Generalized Fibonacci numbers 1. keywords: n−1; |r|; −g1g0 cache: jacodesmath-52.pdf plain text: jacodesmath-52.txt item: #106 of 150 id: jacodesmath-53 author: Bouchat, Rachelle R.; Brown, Tricia Muldoon title: A constructive approach to minimal free resolutions of path ideals of trees date: 2017-01-15 words: 6068 flesch: 79 summary: 12 April 2016 0 Journal of Algebra Combinatorics Discrete Structures and Applications A constructive approach to minimal free resolutions of path ideals of trees Research Article Rachelle R. Bouchat, Tricia Muldoon Brown Abstract: For a rooted tree Γ, we consider path ideals of Γ, which are ideals that are generated by all directed paths of a fixed length in Γ. In this paper, we provide a combinatorial description of the minimal free resolution of these path ideals. 2010 MSC: 05E40 Keywords: Betti numbers, Path ideals, Rooted trees, Monomial ideals 1. keywords: complex; graph; ideals; path; tree; vertex cache: jacodesmath-53.pdf plain text: jacodesmath-53.txt item: #107 of 150 id: jacodesmath-54 author: Geil, Olav; Martin, Stefano; Martínez-Peñas, Umberto; Ruano, Diego title: Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower date: 2017-01-15 words: 5492 flesch: 90 summary: Let q be an even power of a prime, 2√ q−1 ≤ R̃2 ≤ R̃1 < 1, and R̃ = R̃1 − R̃2. 2010 MSC: 94A62, 94B27, 94B65 Keywords: Algebraic geometric codes, Asymptotically good ramp secret sharing schemes, Generalized Hamming weights, Relative generalized Hamming weights, Secret sharing 1. keywords: codes cache: jacodesmath-54.pdf plain text: jacodesmath-54.txt item: #108 of 150 id: jacodesmath-55 author: Jitman, Somphong; Udomkavanich, Patanee title: One–generator quasi–abelian codes revisited date: 2017-01-15 words: 6617 flesch: 87 summary: The characterization and enumeration of quasi-abelian codes have been established in [7]. [7] that a family of quasi-abelian codes contains various new and optimal codes. keywords: abelian; codes; fq[g; generator; quasi; ∈{1 cache: jacodesmath-55.pdf plain text: jacodesmath-55.txt item: #109 of 150 id: jacodesmath-56 author: Sarma, Bhaba Kumar; Sinha, Kalyan title: The nonnegative Q−matrix completion problem date: 2017-01-15 words: 6495 flesch: 75 summary: 2010 MSC: 05C20, 05C50 Keywords: Digraph, Partial matrix, Matrix completion, Nonnegative Q-matrix, Q-completion problem 1. For an extensive survey of matrix completion problems, we refer the relevant sections in Handbook of Linear Algebra [9] published by Chapman and Hall/CRC Press. keywords: completion; digraph; matrix cache: jacodesmath-56.pdf plain text: jacodesmath-56.txt item: #110 of 150 id: jacodesmath-58 author: Oztas, Elif Segah; Yildiz, Bahattin; Siap, Irfan title: On DNA codes from a family of chain rings date: 2017-01-15 words: 5686 flesch: 84 summary: Reversible cyclic codes over R23 of length 6 which correspond to reversible complement DNA codes of length 24. Irfan Siap Abstract: In this work, we focus on reversible cyclic codes which correspond to reversible DNA codes or reversible-complement DNA codes over a family of finite chain rings, in an effort to extend what was done by Yildiz and Siap in [20]. keywords: codes; complement; cyclic; dna; u4 u4 cache: jacodesmath-58.pdf plain text: jacodesmath-58.txt item: #111 of 150 id: jacodesmath-59 author: Leroy, André title: Editor’s note date: 2017-05-15 words: 367 flesch: 51 summary: They cover pure ring theory such as nil *-clean rings, radical classes or algebras such as Grassman algebras and Steenrod algebras and many papers relating these subjects with coding theory such as MacWilliams extension theorem, dual codes, Lee and Hamming weight. Received : 29 December 2016 Journal of Algebra Combinatorics Discrete Structures and Applications Editor’s note André Leroy This special issue contains papers written by participants to the conference Noncommutative rings and their Applications that was held in Lens (France) at the Science faculty of the Université d’Artois. keywords: conference; france cache: jacodesmath-59.pdf plain text: jacodesmath-59.txt item: #112 of 150 id: jacodesmath-6 author: Chang, Chih-Hung title: Some properties of topological pressure on cellular automata date: 2014-09-15 words: 4924 flesch: 80 summary: [5] J.-C. Ban, C.-H. Chang, T.-J. Chen, and M.-S. Lin, The complexity of permutive cellular automata, J. Cell. ,υ − 1} for some υ ≥ 2, and let X = AZ be the space of infinite sequences x = (xi)i∈Z. A continuous map F : X → X satisfying F ◦σ = σ◦F is called a cellular automaton (CA), where σ is the shift map defined by σ(x)i = xi+1, i ∈ Z. CA is a particular class of dynamical systems introduced by keywords: permutive; rule cache: jacodesmath-6.pdf plain text: jacodesmath-6.txt item: #113 of 150 id: jacodesmath-60 author: Szabo, Steve; Wood, Jay A. title: Properties of dual codes defined by nondegenerate forms date: 2017-05-15 words: 4257 flesch: 80 summary: For c ∈ C and a ∈ A, 〈x,c〉a =〈 x,σ−1(a)c 〉 ∈ 〈x,C〉, which implies that 〈x,C〉 is a right ideal. Since ρ is a generating character, Lemma 2.1 implies 〈x,C〉 = 0, showing x ∈ l(C). keywords: code; finite cache: jacodesmath-60.pdf plain text: jacodesmath-60.txt item: #114 of 150 id: jacodesmath-61 author: Abdelghany, Noha; Megahed, Nefertiti title: Code–checkable group rings date: 2017-05-15 words: 5108 flesch: 82 summary: 4(2) • 115–122 Received: 14 June 2015 Accepted: 1 February 2016 Journal of Algebra Combinatorics Discrete Structures and Applications Code–checkable group rings Research Article Noha Abdelghany, Nefertiti Megahed Abstract: A code over a group ring is defined to be a submodule of that group ring. 2010 MSC: 16S34, 16P60 Keywords: Group rings, Pseudo-morphic rings, A-by-B groups, Checkable codes, Pseudo-morphic group rings 1. keywords: code; group; ring cache: jacodesmath-61.pdf plain text: jacodesmath-61.txt item: #115 of 150 id: jacodesmath-62 author: Crivei, Septimiu; Keskin Tütüncü, Derya title: On some radicals and proper classes associated to simple modules date: 2017-05-15 words: 2850 flesch: 77 summary: 4(2) • 123–129 Received: 17 June 2015 Accepted: 5 February 2016 Journal of Algebra Combinatorics Discrete Structures and Applications On some radicals and proper classes associated to simple modules Research Article Septimiu Crivei, Derya Keskin Tütüncü Abstract: For a unitary right module M, there are two known partitions of simple modules in the category σ[M]: the first one divides them into M-injective modules and M-small modules, while the second one divides them into M-projective modules and M-singular modules. We study inclusions between the first two and the last two classes of simple modules in terms of some associated radicals and proper classes. keywords: module; simple; suppl; σ[m cache: jacodesmath-62.pdf plain text: jacodesmath-62.txt item: #116 of 150 id: jacodesmath-63 author: Irwansyah, I; Muchtadi-Alamsyah, Intan; Muchlis, Ahmad; Barra, Aleams; Suprijanto, Djoko title: Codes over an infinite family of algebras date: 2017-05-15 words: 4466 flesch: 90 summary: As we can see, every element a ∈ Bk can be written as a = ∑ S∈2Ω αSvS, for some αS ∈ Fp, where vS = ∏ i∈S vi and v∅ ∈ Bk is a zero divisor if and only if ω ∈ 〈w1,w2, . . . keywords: codes; ring cache: jacodesmath-63.pdf plain text: jacodesmath-63.txt item: #117 of 150 id: jacodesmath-64 author: Dougherty, Steven T.; Vergili, Tane title: Codes and the Steenrod algebra date: 2017-05-15 words: 6569 flesch: 88 summary: We consider linear codes as well as additive codes. Namely, linear codes are when the code is a submodule of the ambient space and additive codes are when they are simply a subgroup of the ambient space in terms of the additive operation. keywords: a(n; algebra; code; dual; left; linear; self; sq2 cache: jacodesmath-64.pdf plain text: jacodesmath-64.txt item: #118 of 150 id: jacodesmath-65 author: Harmancı, Abdullah; Chen, Huanyin; Özcan, A. Çiğdem title: Strongly nil *-clean rings date: 2017-05-15 words: 6142 flesch: 89 summary: ∈ R be an idempotent. Thus, for any x ∈ R, there exists a unique idempotent e ∈ R such that x− e ∈ R is nilpotent. keywords: ideal; projection; ring; ∗-clean cache: jacodesmath-65.pdf plain text: jacodesmath-65.txt item: #119 of 150 id: jacodesmath-66 author: Centrone, Lucio title: On the graded identities of the Grassmann algebra: We survey the results concerning the graded identities of the infinite dimensional Grassmann algebra date: 2017-05-15 words: 7924 flesch: 76 summary: 2010 MSC: 16R10, 16P90, 16S10, 16W50 Keywords: Graded polynomial identities, Grassmann algebra 1. Graded PI-algebras We introduce the terminology for the study of graded polynomial identities. keywords: algebra; characteristic; graded; grassmann; ideal; identities; polynomial; theorem cache: jacodesmath-66.pdf plain text: jacodesmath-66.txt item: #120 of 150 id: jacodesmath-67 author: Chalom, Gladys; Ferraz, Raul A.; Milies, C. Polcino title: Essential idempotents and simplex codes date: 2017-05-15 words: 3827 flesch: 80 summary: [2] S. D. Berman, On the theory of group codes, Kibernetika 3(1) (1967) 31–39. In what follows, we shall show that these are not better than minimal cyclic codes. keywords: abelian; algebra; code; cyclic; group cache: jacodesmath-67.pdf plain text: jacodesmath-67.txt item: #121 of 150 id: jacodesmath-69 author: Boulagouaz, M’hammed; Bouye, Mohamed title: Correspondence between steganographic protocols and error correcting codes date: 2017-05-15 words: 4313 flesch: 78 summary: 4(2) • 197–206 Received: 12 June 2015 Accepted: 29 February 2016 Journal of Algebra Combinatorics Discrete Structures and Applications Correspondence between steganographic protocols and error correcting codes Research Article M’hammed Boulagouaz, Mohamed Bouye Abstract: In this work we present a correspondence between the steganographic systems and error correcting codes. We show that this new protocol has much better parameters than protocols which we get from Hamming codes or from the 2-error-correcting primitive BCH codes, for high levels of incorporation. 2010 MSC: 94A60, 94B29, 94B40 Keywords: Steganographic protocol, Hamming distance, Linear correcting code, Covering radius, Parity matrix, BCH code 1. keywords: protocol; steganographic cache: jacodesmath-69.pdf plain text: jacodesmath-69.txt item: #122 of 150 id: jacodesmath-70 author: Langevin, Philippe; Wood, Jay A. title: The extension problem for Lee and Euclidean weights date: 2017-05-15 words: 6308 flesch: 80 summary: Suppose R = Z/p`+1Z, with p prime. Thus, for i < `, the image of Ui under the projection U ∼= U ×C → C ∼= U/U is the unique subgroup in C of order 2i. keywords: group; ker; prime; theorem; weight cache: jacodesmath-70.pdf plain text: jacodesmath-70.txt item: #123 of 150 id: jacodesmath-71 author: Alghazzawi, Dilshad title: Reversible elements in rings date: 2017-05-15 words: 3809 flesch: 86 summary: ∈ R such that f(x)c = 0. In other words R is semi- commutative if for any elements a,b ∈ R we have ab = 0 implies that aRb = 0. keywords: right; ring; rrev(r cache: jacodesmath-71.pdf plain text: jacodesmath-71.txt item: #124 of 150 id: jacodesmath-72 author: Daskalov, Rumen; Hristov, Plamen title: Some new ternary linear codes date: 2017-09-15 words: 3036 flesch: 81 summary: The new codes. code C1 subcode C2 code C3 new code C [160,12,90]3 [160,10,96]3 [8,2,6]3 [168,12,96]3 [104,13,54]3 The problem of finding the parameters of optimal codes is a very difficult one and has two aspects - one involves the construction of new codes with better minimum distances and the other is proving the nonexistence of codes with given parameters. keywords: code; linear cache: jacodesmath-72.pdf plain text: jacodesmath-72.txt item: #125 of 150 id: jacodesmath-73 author: Musukwa, Augustine I.; Magamba, Kondwani; Ryan, John A. title: Enumeration of extended irreducible binary Goppa codes of degree $2^{m}$ and length $2^{n}+1$ date: 2017-09-15 words: 6759 flesch: 86 summary: The number of fixed affine sets in A Note that the group G defined in Definition 2.7 is a cyclic group of order n2m, where n > 2 is prime, and it’s subgroups are all of the form 〈σk〉, where k is a factor of n2m. Further, note that G acts on A. This is to avoid repetition when we multiply column 3 by column 4 in order to get the total number of fixed affine sets by the elements in G. Table 1. Subgroup Order of No. of elements keywords: affine; m−1; number; o(α cache: jacodesmath-73.pdf plain text: jacodesmath-73.txt item: #126 of 150 id: jacodesmath-74 author: Mahalanobis, Ayan; Singh, Anupam title: Gaussian elimination in split unitary groups with an application to public-key cryptography date: 2017-09-15 words: 7164 flesch: 77 summary: [21] R. Steinberg, Variations on a theme of Chevalley, Pacific J. Math. 9 (1959) 875–891. 260 http://orcid.org/0000-0001-9822-3672 http://orcid.org/0000-0002-6162-4605 http://dx.doi.org/10.1007/978-3-642-15582-6_11 http://dx.doi.org/10.1007/978-3-642-15582-6_11 http://dx.doi.org/10.1007/978-3-642-15582-6_11 http://dx.doi.org/10.1016/j.jsc.2014.08.006 http://dx.doi.org/10.1016/j.jsc.2014.08.006 http://dx.doi.org/10.1006/jsco.1996.0125 http://dx.doi.org/10.1006/jsco.1996.0125 http://dx.doi.org/10.1016/S0747-7171(02)00132-3 http://dx.doi.org/10.1016/S0747-7171(02)00132-3 https://doi.org/10.1112/S1461157000000437 https://doi.org/10.1112/S1461157000000437 https://doi.org/10.1090/S0025-5718-03-01582-5 https://doi.org/10.1090/S0025-5718-03-01582-5 http://www.ams.org/mathscinet-getitem?mr=45125 http://www.ams.org/mathscinet-getitem?mr=45125 http://www.ams.org/mathscinet-getitem?mr=2839923 http://www.ams.org/mathscinet-getitem?mr=2839923 http://www.ams.org/mathscinet-getitem?mr=1859189 http://www.ams.org/mathscinet-getitem?mr=1859189 http://www.ams.org/mathscinet-getitem?mr=780184 http://www.ams.org/mathscinet-getitem?mr=1804385 http://www.ams.org/mathscinet-getitem?mr=1804385 http://dx.doi.org/10.1016/j.jalgebra.2009.04.028 http://dx.doi.org/10.1016/j.jalgebra.2009.04.028 http://dx.doi.org/10.1080/00927872.2011.602998 http://dx.doi.org/10.1080/00927872.2011.602998 http://dx.doi.org/10.1080/00927872.2014.974254 https://doi.org/10.1112/S0024611598000422 https://doi.org/10.1112/S0024611598000422 http://www.ams.org/mathscinet-getitem?mr=2858866 http://www.ams.org/mathscinet-getitem?mr=2858866 http://dx.doi.org/10.1007/3-540-44647-8_28 http://dx.doi.org/10.1007/3-540-44647-8_28 http://www.ams.org/mathscinet-getitem?mr=1452069 http://www.ams.org/mathscinet-getitem?mr=1452069 http://www.ams.org/mathscinet-getitem?mr=109191 Introduction Unitary groups Elementary matrices and elementary operations in unitary groups Gaussian elimination in unitary group Some lemmas Finite unitary groups The MOR cryptosystem on unitary groups Conclusion References [2] H. Bäärnhielm, D. Holt, C. R. Leedham-Green, E. A. O’Brien, A practical model for computation with matrix groups, J. Symb. keywords: algorithm; case; elementary; groups; matrices; matrix; unitary cache: jacodesmath-74.pdf plain text: jacodesmath-74.txt item: #127 of 150 id: jacodesmath-75 author: Guenda, Kenza; Gulliver, T. Aaron title: On the equivalence of cyclic and quasi-cyclic codes over finite fields date: 2017-09-15 words: 4416 flesch: 84 summary: Thus for T l ∈ P we have σ−1T lσ ∈ P , so that NSn(P) ⊂ H ′(P). Further, the set of Brand is extended to the class of quasi-cyclic codes of length prl. keywords: codes; cyclic; equivalence; length; subgroup cache: jacodesmath-75.pdf plain text: jacodesmath-75.txt item: #128 of 150 id: jacodesmath-76 author: Leopardi, Paul title: Twin bent functions, strongly regular Cayley graphs, and Hurwitz-Radon theory date: 2017-09-15 words: 4439 flesch: 74 summary: In that paper, these isomorphisms and the characterization of Cay(σm) and Cay(τm) as Cayley graphs of bent functions are used to prove the following theorem. What is the relationship between other classifications of bent functions and the classifi- cation via Cayley graphs? keywords: bent; functions; graph; matrices; paper; theorem cache: jacodesmath-76.pdf plain text: jacodesmath-76.txt item: #129 of 150 id: jacodesmath-77 author: Cuén-Ramos, Jesús E.; Vega, Gerardo title: A class of cyclic codes constructed via semiprimitive two-weight irreducible cyclic codes date: 2017-09-15 words: 4901 flesch: 79 summary: [3] T. Helleseth, Some two–weight codes with composite parity–check polynomials, IEEE Trans. [6] G. Vega, Two–weight cyclic codes constructed as the direct sum of two one–weight cyclic codes, Finite Fields Appl. 14(3) (2008) 785–797. keywords: codes; cyclic; k−1; theorem; weight cache: jacodesmath-77.pdf plain text: jacodesmath-77.txt item: #130 of 150 id: jacodesmath-78 author: Araya, Makoto; Harada, Masaaki; Suzuki, Yuichi title: Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$ date: 2018-01-15 words: 1920 flesch: 71 summary: [4] M. Harada, A. Munemasa, On the classification of weighing matrices and self–orthogonal codes, J. Combin. The minimum non-zero weight of all codewords in C is called the minimum weight of C. Two codes C and C′ are equivalent if there is a (0, 1,−1)-monomial matrix P with C′ = C · keywords: codes; length; self; weight cache: jacodesmath-78.pdf plain text: jacodesmath-78.txt item: #131 of 150 id: jacodesmath-79 author: Palines, Herbert S.; Jitman, Somphong; Dela Cruz, Romar B. title: Hermitian self-dual quasi-abelian codes date: 2018-01-15 words: 7996 flesch: 82 summary: 6 April 2017 Journal of Algebra Combinatorics Discrete Structures and Applications Hermitian self-dual quasi-abelian codes Research Article Herbert S. Palines, Somphong Jitman, Romar B. Dela Cruz Abstract: Quasi-abelian codes constitute an important class of linear codes containing theoretically and prac- tically interesting codes such as quasi-cyclic codes, abelian codes, and cyclic codes. Quasi-abelian codes serve as the general case for quasi-cyclic codes (if H 6= G is cyclic), abelian codes (if H = G), and cyclic codes (if H = G is cyclic). keywords: abelian; codes; dual; hermitian; quasi; self; type cache: jacodesmath-79.pdf plain text: jacodesmath-79.txt item: #132 of 150 id: jacodesmath-8 author: Chen, Eric Z.; Aydin, Nuh title: A database of linear codes over F_13 with minimum distance bounds and new quasi-twisted codes from a heuristic search algorithm date: 2015-01-15 words: 8893 flesch: 77 summary: With the help of modern computers, many record-breaking QC and QT codes have been constructed [2]-[13]. The online database of QT codes contains best-known QC and QT codes [24]. keywords: bounds; codes; f13; linear; linear codes; minimum; new; qt codes; table cache: jacodesmath-8.pdf plain text: jacodesmath-8.txt item: #133 of 150 id: jacodesmath-80 author: Kok, Johan; Bej, Saptarshi title: Coloring sums of extensions of certain graphs date: 2018-01-15 words: 5749 flesch: 80 summary: 5(1) • 19–27 Received: 23 January 2017 Accepted: 26 June 2017 Journal of Algebra Combinatorics Discrete Structures and Applications Coloring sums of extensions of certain graphs Research Article Johan Kok, Saptarshi Bej Abstract: We recall that the minimum number of colors that allow a proper coloring of graph G is called the chromatic number of G and denoted χ(G). We recall that the minimum number of colors that allow a proper coloring of graph G is called the chromatic number of G and denoted χ(G). keywords: coloring; graph; vertices cache: jacodesmath-80.pdf plain text: jacodesmath-80.txt item: #134 of 150 id: jacodesmath-82 author: Horlemann-Trautmann, Anna-Lena; Kuijper, Margreta title: A module minimization approach to Gabidulin decoding via interpolation date: 2018-01-15 words: 7939 flesch: 76 summary: Note that in [13] minimal bases were addressed as minimal Gröbner bases. Subsection 2.3 deals with modules over the ring of linearized polynomials and draws attention to minimal bases of these modules and their Predictable Leading Monomial property. keywords: algorithm; basis; decoding; gabidulin; lq(x; module; polynomial cache: jacodesmath-82.pdf plain text: jacodesmath-82.txt item: #135 of 150 id: jacodesmath-84 author: Julian, Michael Ryan title: No MacWilliams duality for codes over nonabelian groups date: 2018-01-15 words: 2556 flesch: 71 summary: In particular, they asked “Is there a subclass of nonabelian groups for which a duality and a MacWilliams formula exist?” We will answer this question under the assumption that a code over a group G is defined to be a subgroup of Gn, in analogy to the usual definition of codes over abelian groups. [3] have asked whether there is a duality theory and a MacWilliams formula for codes over nonabelian groups, or more generally, whether there is any subclass of nonabelian groups which have such a duality theory. keywords: dual; group; lattice; nonabelian; subgroup cache: jacodesmath-84.pdf plain text: jacodesmath-84.txt item: #136 of 150 id: jacodesmath-85 author: Singh, Gurmail title: Fourier matrices of small rank date: 2018-05-15 words: 8128 flesch: 81 summary: Therefore, the structure constant N111 is integer only for n = 1, and the associated Fourier matrix S = 1 √ 2 [ 1 n 1 −1 ] . Note that, a C-algebra arising from a Fourier matrix S is a symmetric C-algebra if and only if S is a real matrix. keywords: algebra; fourier; matrix cache: jacodesmath-85.pdf plain text: jacodesmath-85.txt item: #137 of 150 id: jacodesmath-86 author: Chen, Eric Z. title: Some new binary codes with improved minimum distances date: 2018-05-15 words: 3005 flesch: 71 summary: In section 3, new binary QC codes that improve the minimum distance in [13] are given, and the well-known Construction X is applied to produce 2 more binary linear codes. The well-known Construction X is a simple and efficient method to construct new codes by combining 3 codes. keywords: binary; codes; generator cache: jacodesmath-86.pdf plain text: jacodesmath-86.txt item: #138 of 150 id: jacodesmath-87 author: Fornasiero, Federico; Tizziotti, Guilherme title: The root diagram for one-point AG codes arising from certain curves with separated variables date: 2018-05-15 words: 6883 flesch: 86 summary: So, Proposition 3.3 and Theorem 3.4 (where a = 5, b = 3, ρ1 = 4, ρ2 = 3, ρ3 = 2 and λ = 30) give the following root diagram. α2 α4 α6 α8 α10 α12 α14 α16 α18 α20 α22 1 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Acknowledgment: The authors would like to thank the anonymous referees for very useful com- ments and suggestions that improved the presentation of this work. yq + y = xm, see [13]; and curves on Kummer extensions, see [2]. keywords: basis; codes; curve; diagram; gröbner; root cache: jacodesmath-87.pdf plain text: jacodesmath-87.txt item: #139 of 150 id: jacodesmath-88 author: Visweswaran, Subramanian; Parejiya, Jaydeep title: Some results on the comaximal ideal graph of a commutative ring date: 2018-05-15 words: 12260 flesch: 90 summary: Let I be an ideal of a ring R. Then the annihilator of I in R, denoted by AnnRI is defined as AnnRI = {r ∈ R|Ir Let R be a ring such that R admits at least two maximal ideals. keywords: graph; ring; |max(r)| cache: jacodesmath-88.pdf plain text: jacodesmath-88.txt item: #140 of 150 id: jacodesmath-89 author: Kumegawa, Kazuki; Maruta, Tatsuya title: Non–existence of some 4–dimensional Griesmer codes over finite fields date: 2018-05-15 words: 10905 flesch: 94 summary: − q − 1), (C) (τq−2,τq−1,τ2q−3,τ2q−2,τ2q−1) = (1, 2, 1, 2q−1,q2−q−2), (D) (τq−1,τ2q−3,τ2q−2,τ2q−1) = (3, 1, 2q,q2−q−3), or (E) (τq−1,τ2q−3,τ2q−1) Let C be a putative [n = 2q3 − (r − 2)q2 − rq − (r − 3), 4,d = 2q3 − rq2 − 2q + 2]q code with 3 ≤ r ≤ (q+ 1)/2, q ≥ 5. keywords: q −; q2 −; r − cache: jacodesmath-89.pdf plain text: jacodesmath-89.txt item: #141 of 150 id: jacodesmath-9 author: Shende, Anil M. title: Maximal induced paths and minimal percolating sets in hypercubes date: 2015-01-15 words: 4930 flesch: 81 summary: Several properties of maximal snakes have been found useful in establishing better bounds on the lengths of longest snakes in hypercubes We study the relationship between maximal snakes and minimal percolating sets (under 2-bootstrap percolation) in hypercubes. keywords: percolating; set; snake; vertex cache: jacodesmath-9.pdf plain text: jacodesmath-9.txt item: #142 of 150 id: jacodesmath-90 author: Rajeswari, Kota Nagalakshmi; Gupta, Umesh title: Characterization of $2\times 2$ nil-clean matrices over integral domains date: 2018-09-15 words: 5326 flesch: 87 summary: [6] S. Breaz, G. Călugăreanu, P. Danchev, T. Micu, Nil–clean matrix rings, Linear Algebra Appl. 439(10) (2013) 3115–3119. Since trace and determinant of a nil-potent matrix are always zero, a + d = 0 and bc − ad = 0 i.e., d = −a and bc + a2 = 0. keywords: clean; equation; matrix; nil; solution cache: jacodesmath-90.pdf plain text: jacodesmath-90.txt item: #143 of 150 id: jacodesmath-91 author: Bokhary, Syed Ahtsham Ul Haq; Iqbal, Tanveer; Ali, Usman title: Game chromatic number of Cartesian and corona product graphs date: 2018-09-15 words: 4170 flesch: 81 summary: We shall also use the convention that color numbers are only used to differentiate distinct colors, and should not be regarded as ascribed to particular colors. Alice has winning strategy for k colors. keywords: alice; bob; case; color; game; vertex; vertices cache: jacodesmath-91.pdf plain text: jacodesmath-91.txt item: #144 of 150 id: jacodesmath-93 author: Anev, Damyan; Harada, Masaaki; Yankov, Nikolay title: New extremal singly even self-dual codes of lengths 64 and 66 date: 2018-09-15 words: 3815 flesch: 83 summary: [15] H.-P. Tsai, Extremal self–dual codes of lengths 66 and 68, IEEE Trans. [5] P. Çomak, J. L. Kim, F. Özbudak, New cubic self–dual codes of length 54,60 and 66, Appl. keywords: codes; dual; extremal; self; weight cache: jacodesmath-93.pdf plain text: jacodesmath-93.txt item: #145 of 150 id: jacodesmath-94 author: Baumbaugh, Travis Alan; Diaz, Yariana; Friesenhahn, Sophia; Manganiello, Felice; Vetter, Alexander title: Batch Codes from Hamming and Reed-Muller Codes date: 2018-09-15 words: 7677 flesch: 85 summary: 5(3) • 153–165 Received: 24 October 2017 Accepted: 5 September 2018 Journal of Algebra Combinatorics Discrete Structures and Applications Batch codes from Hamming and Reed-Muller codes∗ Research Article Travis Baumbaugh, Yariana Diaz, Sophia Friesenhahn, Felice Manganiello, Alexander Vetter Abstract: Batch codes, introduced by Ishai et al., encode a string x ∈ Σk into an m-tuple of strings, called buckets. In this paper we consider multiset batch codes wherein a set of t-users wish to access one bit of information each from the original string. keywords: batch; codes; muller; reed cache: jacodesmath-94.pdf plain text: jacodesmath-94.txt item: #146 of 150 id: jacodesmath-95 author: Singh, Manjit; Batra, Sudhir title: Weight distribution of a class of cyclic codes of length $2^n$ date: 2020-04-09 words: 6067 flesch: 85 summary: 2010 MSC: 12E05, 12E20, 94B05, 11T71 Keywords: Linear codes, Reversible codes, Weight distributions, Constant weight codes 1. If all the codewords of a code C carry the same weight, then C is called constant weight code. keywords: 2k−1; codes; weight cache: jacodesmath-95.pdf plain text: jacodesmath-95.txt item: #147 of 150 id: jacodesmath-96 author: Aydin, Nuh; Foret, Derek title: New Linear Codes over $GF(3)$, $GF(11)$, and $GF(13)$ date: 2019-01-15 words: 3576 flesch: 77 summary: 2010 MSC: 94B15, 94B60 Keywords: Best known codes, Constacyclic codes, Quasi-cyclic codes, Quasi-twisted codes 1. The class of cyclic codes and its various generalizations, such as constacyclic codes, quasi-cyclic (QC) codes, and quasi- twisted (QT) codes, lend themselves well to the problem of finding codes with good parameters. keywords: codes; constacyclic; linear cache: jacodesmath-96.pdf plain text: jacodesmath-96.txt item: #148 of 150 id: jacodesmath-97 author: Unnithan, Sunil Kumar Raghavan; Balakrishnan, Kannan title: Betweenness centrality in convex amalgamation of graphs date: 2019-01-15 words: 8253 flesch: 86 summary: + k − 2p + 1) and the vertices from uα+k+1 to uβ contribute 1 2 (p − k − 2)(n − p − k − 1) and no more vertex from the right. (c) Consider the vertex ur for 1 ≤ r < α, now the vertices lying between ur and uα make pairs with all vertices of V giving the contribution (m 2 − p − r)(n − p). keywords: b b; betweenness; graph; vertex; vertices; − p cache: jacodesmath-97.pdf plain text: jacodesmath-97.txt item: #149 of 150 id: jacodesmath-98 author: Aydogdu, Ismail title: Codes over $\mathbb{Z}_{p}[u]/{\langle u^r \rangle}\times\mathbb{Z}_{p}[u]/{\langle u^s \rangle}$ date: 2019-01-15 words: 4815 flesch: 86 summary: Since this family of linear codes has been introduced recently many more properties of these families of codes await explorations, such as cyclicity. [6] A. Bonnecaze, P. Udaya, Cyclic codes and self–dual codes over F2 +uF2, IEEE Trans. keywords: codes; generator; matrix; u u; us]-linear cache: jacodesmath-98.pdf plain text: jacodesmath-98.txt item: #150 of 150 id: jacodesmath-99 author: Tout, Omar title: Some explicit expressions for the structure coefficients of the center of the symmetric group algebra involving cycles of length three date: 2019-05-15 words: 4530 flesch: 86 summary: = pλ, where β = (ai−1,ai,b). = pλ. keywords: coefficients; cycle cache: jacodesmath-99.pdf plain text: jacodesmath-99.txt