Explicit factorization of x1lm1l2m2l3m3 - a and a-constacyclic codes over a finite field

被引：0

作者：

Rakphon, Supakarn ^{[1
]}

Chongchitmate, Wutichai ^{[1
]}

Phuto, Jirayu ^{[2
]}

Klin-eam, Chakkrid ^{[2
]}

机构：

[1] Chulalongkorn Univ, Fac Sci, Dept Math & Comp Sci, Bangkok, Thailand

[2] Naresuan Univ, Fac Sci, Dept Math, Phitsanulok, Thailand

来源：

COMMUNICATIONS IN ALGEBRA | 2022年 / 50卷 / 11期

关键词：

Constacyclic codes; cyclotomic coset; generator polynomials; irreducible factor polynomials;

D O I：

10.1080/00927872.2022.2072854

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let F-q be a finite field of order q, t be a prime and m(1), m(2), m(3) be positive integers. In this article, we find all irreducible divisors of x(1)(lm1l2m2l3m3) - a over F-q where a is an element of F-q* and q(t) - 1 = l(1)(V1)l(2)(V2)l(3)(V3) c such that l(1), l(2), l(3) are distinct odd primes and c is a positive integer with gcd(l(1) l(2) l(3), c) = 1 and gcd(l(1)l(2)l(3), q(q - 1)) = 1. Moreover, we construct an a-constacyclic code by using these irreducible divisors.

引用

页码：4725 / 4745

页数：21

共 50 条

[1] Explicit factorization of X2mpn-1 over a finite field
Chen, Bocong
Li, Liangchen
Tuerhong, Rouziwanguli
FINITE FIELDS AND THEIR APPLICATIONS, 2013, 24 : 95 - 104
[2] The minimum Hamming distances of the irreducible cyclic codes of length l(1)(m1) l(2)(m2) ... l(r)(mr)
Pruthi, Manju
Pankaj
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2016, 19 (5-6): : 965 - 995
[3] The Characterization of Finite Simple Groups,L3(32m-1)(m 2),by Their Element Orders
Ming Chun XUDepartment of Mathematics
Acta Mathematica Sinica(English Series), 2005, 21 (04) : 899 - 902
[4] The Characterization of Finite Simple Groups, L3(32m–1)(m ≥ 2), by Their Element Orders
Ming Chun Xu
Acta Mathematica Sinica, 2005, 21 : 899 - 902
[5] The characterization of finite simple groups, L3(32m-1)(m ≥ 2), by their element orders
Xu, MC
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2005, 21 (04) : 899 - 902
[6] X-decomposable finite groups for X={1, m, m + 1, m + 2}
R. Chen
X. Guo
K. P. Shum
Siberian Mathematical Journal, 2017, 58 : 899 - 906
[7] A note on the diophantine equation (m(3)-3m)(x)+(3m(2)-1)(y)=((m)2+1)(z)
Le, MH
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1997, 73 (07) : 148 - 149
[8] Efficient multiplication in F3lm, m≥1 and 5≤l≤18
Cenk, Murat
Ozbudak, Ferruh
PROGRESS IN CRYPTOLOGY - AFRICACRYPT 2008, 2008, 5023 : 406 - +
[9] Type 2 constacyclic codes over F2m[u]/⟨u3⟩ of oddly even length
Cao, Yuan
Cao, Yonglin
Dinh, Hai Q.
Fu, Fang-Wei
Gao, Yun
Sriboonchitta, Songsak
DISCRETE MATHEMATICS, 2019, 342 (02) : 412 - 426
[10] On the exponential diophantine equation (m3-3m)x+(3m2-1)y=(m2+1)z
Le, MH
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2001, 58 (03): : 461 - 466

← 1 2 3 4 5 →