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Mathematical Problems of Computer Science 31, 5{15, 2008.

On a Class of I r r educible P olynomials Over Fp
Me ls ik K . K yu r e g ya n , E d it a Y u . H a r u t yu n ya n a n d Mika ye l G. E vo ya n y

Institute for Informatics and Automation Problems of NAS of RA
yFaculty of Informatics and Applied Mathematics, Yerevan State University

email: edita@ipia.sci.am, email:michael.ipm@gmail.com

Abstract

The paper presents some results regarding constructive theory of synthesis of ir-
reducible polynomials of degree pt over Fp from the given primitive elements in Fp,
where p is an odd prime and t is an integer whose prime factors all divide p ¡ 1.

Keywor ds p r im it ive p o lyn o m ia l, e xp lic it ly c o n s t r u c t e d s e qu e n c e s , p e r io d , lin e a r o p e r a t o r ,
p r im it ive e le m e n t

Refer ences

[1 ] A lb e r t A .A ., F undamental Concepts of Higher Algebra, U n ive r s it y o f Ch ic a g o P r e s s ,
Ch ic a g o , 1 9 5 6 .

[2 ] P e t e r s o n W . W ., W e ld o n E . I. E rror-Correcting Codes, 2 n d e d ., M.I.T. P r e s s , Ca m -
b r id g e , Ma s s ., 1 9 7 2 .

[3 ] V a r s h a m o v R .R . On a m e t h o d o f c o n s t r u c t in g ir r e d u c ib le p o lyn o m ia ls o ve r ¯ n it e ¯ e ld s .
D okladi Akademii Nauk of Armenia, vo l. 7 9 , N o .1 , 1 9 8 4 , p p . 2 6 { 2 8 ( in R u s s ia n ) .

Fp ¹³ßïÇ íñ³ ³Ýí»ñͳݻÉÇ µ³½Ù³Ý¹³ÙÝ»ñÇ ÙÇ ¹³ëÇ Ù³ëÇÝ
Ø. ÎÛáõñ»ÕÛ³Ý, Ø. ¾íáÛ³Ý, ¾. гñáõÃÛáõÝÛ³Ý

²Ù÷á÷áõÙ

Ðá¹í³ÍáõÙ Ý»ñϳ۳óí³Í »Ý ÙÇ ß³ñù ³ñ¹ÛáõÝùÝ»ñ, áñáÝù ³éÝãíáõÙ »Ý ³Ýí»ñ³Í»ÉÇ
µ³½Ù³Ý¹³ÙÝ»ñÇ ëÇÝû½Ç ÏáÝëïñáõÏïÇí ï»ëáõÃÛ³ÝÁ, Ù³ëݳíáñ³å»ë Fp ¹³ßïÇ íñ³
pt ³ëïÇ׳ÝÇ ³Ýí»ñ³Í»ÉÇ µ³½Ù³Ý¹³ÙÝ»ñÇ Ï³éáõóÙ³ÝÁ û·ï³·áñÍ»Éáí Fp ¹³ßïÇ
åñÇÙÇïÇí ¾É»Ù»ÝïÝ»ñÁ, áñï»Õ p-Ý å³ñ½ Ï»Ýï ÃÇí ¿, ÇëÏ t-Ý ³ÙµáÕç ÃÇí ¿, áñÇ µáÉáñ
å³ñ½ µ³½Ù³å³ïÏÇãÝ»ñÁ µ³Å³ÝáõÙ »Ý p ¡ 1 ÃÇíÁ :

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