A class of linear codes of length 2 over finite chain rings

被引：19

作者：

Cao, Yonglin ^{[1
]}

Cao, Yuan ^{[1
,2
]}

Dinh, Hai Q. ^{[3
,4
]}

Fu, Fang-Wei ^{[5
,6
]}

Gao, Jian ^{[1
]}

Sriboonchitta, Songsak ^{[7
]}

机构：

[1] Shandong Univ Technol, Sch Math & Stat, Zibo 255091, Shandong, Peoples R China

[2] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China

[3] Ton Duc Thang Univ, Div Computat Math & Engn, Inst Computat Sci, Ho Chi Minh City, Vietnam

[4] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[5] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[6] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

[7] Chiang Mai Univ, Fac Econ, Chiang Mai 52000, Thailand

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Linear codes; constacyclic codes; generator matrix; finite chain rings; PLUS ALPHA-U(2))-CONSTACYCLIC CODES; ROOT CONSTACYCLIC CODES; COMPLETE CLASSIFICATION; NEGACYCLIC CODES; CYCLIC CODES;

D O I：

10.1142/S0219498820501030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F-pm be a finite field of cardinality p(m), where p is an odd prime, k, lambda be positive integers satisfying lambda >= 2, and denote K= Fp(m) [x]/ < f (x)(lambda pk)>, where f (x) is an irreducible polynomial in F-pm [a]. In this note, for any fixed invertible element omega is an element of K-x, we present all distinct linear codes S over K of length 2 satisfying the condition: (omega f (x)p(k) a(1), a(0)) is an element of S for all (a(0), a(1)) is an element of S. This conclusion can be used to determine the structure of (delta + alpha u(2))-constacyclic codes over the finite chain ring F-pm [u]/< u(2 lambda)> of length np(k) for any positive integer n satisfying gcd(p, n) = 1.

引用

页数：15

共 23 条

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FINITE FIELDS AND THEIR APPLICATIONS, 2018, 50 :1-16

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