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

[1] THE DETERMINATION OF THE GROUP OF AUTOMORPHISMS OF A FINITE CHAIN RING OF CHARACTERISTIC-P [J].

ALKHAMEES, Y .

QUARTERLY JOURNAL OF MATHEMATICS, 1991, 42 (168) :387-391

[2]

Assmus E. F. Jr., 1969, Journal of Combinatorial Theory, Series A, V6, P122, DOI 10.1016/S0021-9800(69)80115-8

[3] Applications of coding theory to the construction of modular lattices [J].

Bachoc, C .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1997, 78 (01) :92-119

[4]

Berlekamp E., 1967, P C COMB MATH ITS AP, P298

[5]

Berlekamp ER., 2015, Algebraic coding theory, Vrevised

[6] Cyclic codes over Z4 of oddly even length [J].

Blackford, T .

DISCRETE APPLIED MATHEMATICS, 2003, 128 (01) :27-46

[7] Quantum error correction via codes over GF (4) [J].

Calderbank, AR ;

Rains, EM ;

Shor, PW ;

Sloane, NJA .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (04) :1369-1387

[8] A LINEAR CONSTRUCTION FOR CERTAIN KERDOCK AND PREPARATA CODES [J].

CALDERBANK, AR ;

HAMMONS, AR ;

KUMAR, PV ;

SLOANE, NJA ;

SOLE, P .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 29 (02) :218-222

[9] Constacyclic codes of length 2ps over Fpm + uFpm [J].

Chen, Bocong ;

Dinh, Hai Q. ;

Liu, Hongwei ;

Wang, Liqi .

FINITE FIELDS AND THEIR APPLICATIONS, 2016, 37 :108-130

[10] Application of Constacyclic Codes to Quantum MDS Codes [J].

Chen, Bocong ;

Ling, San ;

Zhang, Guanghui .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2015, 61 (03) :1474-1484

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