Explicit factorization of X2mpn-1 over a finite field

被引：23

作者：

Chen, Bocong ^{[1
]}

Li, Liangchen ^{[2
]}

Tuerhong, Rouziwanguli ^{[3
]}

机构：

[1] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637616, Singapore

[2] Luoyang Normal Univ, Sch Math Sci, Luoyang 471022, Peoples R China

[3] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2013年 / 24卷

基金：

中国国家自然科学基金;

关键词：

Irreducible factorization; Cyclic code; Binomial; Trinomial; DICKSON POLYNOMIALS; CYCLIC CODES;

D O I：

10.1016/j.ffa.2013.06.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F-q be a finite field of odd order q and m, n be positive integers. In this paper, the irreducible factorization of X-2m P-n - 1 over Fq is given in a very explicit form, where p is an odd prime divisor of q-1. It is shown that all the irreducible factors of (XPn)-P-2m - 1 over F-q are either binomials or trinomials. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：95 / 104

页数：10

共 50 条

[1] Explicit factorization of x1lm1l2m2l3m3 - a and a-constacyclic codes over a finite field
Rakphon, Supakarn
Chongchitmate, Wutichai
Phuto, Jirayu
Klin-eam, Chakkrid
COMMUNICATIONS IN ALGEBRA, 2022, 50 (11) : 4725 - 4745
[2] FACTORIZATION OF IRREDUCIBLE POLYNOMIALS OVER A FINITE FIELD WITH SUBSTITUTION XPR - X FOR X
LONG, AF
DUKE MATHEMATICAL JOURNAL, 1973, 40 (01) : 63 - 76
[3] FACTORIZATION OF IRREDUCIBLE POLYNOMIALS OVER A FINITE FIELD WITH SUSTITUTION XQR-X FOR X .1.
LONG, AF
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (07): : A786 - A786
[4] FACTORIZATION OF IRREDUCIBLE POLYNOMIALS OVER A FINITE FIELD WITH SUBSTITUTION XPR-X FOR X .2.
LONG, AF
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (01): : A62 - A62
[5] The set of representatives and explicit factorization of xn-1 over finite fields
Singh, Manjit
Deepak
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2025, 24 (07)
[6] Further factorization of xn-1 over a finite field
Wu, Yansheng
Yue, Qin
Fan, Shuqin
FINITE FIELDS AND THEIR APPLICATIONS, 2018, 54 : 197 - 215
[7] Further factorization of xn - 1 over a finite field (II)
Wu, Yansheng
Yue, Qin
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2021, 13 (06)
[8] FACTORIZATION OF A SPECIAL POLYNOMIAL OVER A FINITE FIELD
CARLITZ, L
PACIFIC JOURNAL OF MATHEMATICS, 1970, 32 (03) : 603 - &
[9] FACTORIZATION OF Q(H(T)(X)) OVER A FINITE-FIELD WHERE Q(X) IS IRREDUCIBLE AND H(T)(X) IS LINEAR .1.
LONG, AF
VAUGHAN, TP
LINEAR ALGEBRA AND ITS APPLICATIONS, 1976, 13 (03) : 207 - 221
[10] An explicit construction of the metaplectic representation over a finite field
Neuhauser, M
JOURNAL OF LIE THEORY, 2002, 12 (01) : 15 - 30

← 1 2 3 4 5 →