ON σ-SELF-ORTHOGONAL CONSTACYCLIC CODES OVER Fpm + uFPm

被引：5

作者：

Liu, Hongwei ^{[1
]}

Liu, Jingge ^{[1
]}

机构：

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

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2022年 / 16卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Constacyclic code; repeated-root code; sigma-self-orthogonal code; sigma-self-dual code; finite commutative chain ring; NEGACYCLIC CODES; CYCLIC CODES; LENGTH 2(S); CONSTRUCTION; PREPARATA; KERDOCK; Z(4);

D O I：

10.3934/amc.2020127

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we generalize the notion of self-orthogonal codes to sigma-self-orthogonal codes over an arbitrary finite ring. Then, we study the sigma-self-orthogonality of constacyclic codes of length p(s) over the finite commutative chain ring F-pm+ uF(pm) , where p is a prime, u(2) = 0 and sigma is an arbitrary ring automorphism of F-pm + uF(pm) . We characterize the structure of sigma-dual code of a lambda-constacyclic code of length p(s) over F-pm + uF(pm). Further, the neces-sary and sufficient conditions for a lambda-constacyclic code to be sigma-self-orthogonal are provided. In particular, we determine all sigma-self-dual constacyclic codes of length p(s) over F-pm + uF(pm). In the end of this paper, when p is an odd prime, we extend the results to constacyclic codes of length 2p(s).

引用

页码：643 / 665

页数：23

共 27 条

[21] Galois hulls of linear codes over finite fields [J].

Liu, Hongwei ;

Pan, Xu .

DESIGNS CODES AND CRYPTOGRAPHY, 2020, 88 (02) :241-255

[22] Some Repeated-Root Constacyclic Codes Over Galois Rings [J].

Liu, Hongwei ;

Maouche, Youcef .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2017, 63 (10) :6247-6255

[23] New entanglement-assisted quantum codes from k-Galois dual codes [J].

Liu, Xiusheng ;

Yu, Long ;

Hu, Peng .

FINITE FIELDS AND THEIR APPLICATIONS, 2019, 55 :21-32

[24] Galois LCD codes over finite fields [J].

Liu, Xiusheng ;

Fan, Yun ;

Liu, Hualu .

FINITE FIELDS AND THEIR APPLICATIONS, 2018, 49 :227-242

[25]

Nechaev A.A., 1991, Discrete Mathematics and Applications, V1, P365

[26]

Pless V., 1972, Discrete Mathematics, V3, P209, DOI 10.1016/0012-365X(72)90034-9

[27] Cyclic and negacyclic codes over the Galois ring GR(p2, m) [J].

Sobhani, R. ;

Esmaeili, M. .

DISCRETE APPLIED MATHEMATICS, 2009, 157 (13) :2892-2903

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