Additive cyclic codes over finite commutative chain rings

被引：6

作者：

Martinez-Moro, Edgar ^{[1
]}

Otal, Kamil ^{[2
,3
]}

Ozbudak, Ferruh ^{[2
,3
]}

机构：

[1] Univ Valladolid, Math Res Inst, Castilla, Spain

[2] Middle East Tech Univ, Dept Math, Dumlupmar Bulvari 1, TR-06800 Ankara, Turkey

[3] Middle East Tech Univ, Inst Appl Math, Dumlupmar Bulvari 1, TR-06800 Ankara, Turkey

来源：

DISCRETE MATHEMATICS | 2018年 / 341卷 / 07期

关键词：

Cyclic codes; Additive codes; Codes over rings; Finite commutative chain rings; Galois rings; MULTIVARIABLE CODES; GALOIS RINGS; CONSTRUCTION; PREPARATA; KERDOCK;

D O I：

10.1016/j.disc.2018.03.016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Additive cyclic codes over Galois rings were investigated in Cao et al. (2015). In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative chain rings, we observe two different kinds of additivity. One of them is a natural generalization of the study in Cao et al. (2015), whereas the other one has some unusual properties especially while constructing dual codes. We interpret the reasons of such properties and illustrate our results giving concrete examples. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：1873 / 1884

页数：12

共 50 条

[1] γ-Dual Codes over Finite Commutative Chain Rings
Dinh, Hai Q.
Thi, Hiep L.
Tansuchat, Roengchai
AXIOMS, 2024, 13 (10)
[2] Notes on Linear Codes over Finite Commutative Chain Rings
Zi-hui Liu Department of Mathematics
Acta Mathematicae Applicatae Sinica(English Series), 2011, 27 (01) : 141 - 148
[3] Notes on linear codes over finite commutative chain rings
Zi-hui Liu
Acta Mathematicae Applicatae Sinica, English Series, 2011, 27 : 141 - 148
[4] Notes on linear codes over finite commutative chain rings
Liu, Zi-hui
ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2011, 27 (01): : 141 - 148
[5] Cyclic and negacyclic codes over finite chain rings
Dinh, HQ
López-Permouth, SR
IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (08) : 1728 - 1744
[6] On the lattice of cyclic codes over finite chain rings
Fotue-Tabue, Alexandre
Mouaha, Christophe
ALGEBRA AND DISCRETE MATHEMATICS, 2019, 27 (02): : 252 - 268
[7] Constacyclic and cyclic codes over finite chain rings
QIAN Jian-fa
The Journal of China Universities of Posts and Telecommunications, 2009, 16 (03) : 122 - 125
[8] Contraction of cyclic codes over finite chain rings
Tabue, Alexandre Fotue
Mouaha, Christophe
DISCRETE MATHEMATICS, 2018, 341 (06) : 1722 - 1731
[9] Constacyclic and cyclic codes over finite chain rings
National Key Laboratory, ISN, Xidian University, Xi'an, 710071, China
J. China Univ. Post Telecom., 2009, 3 (122-125):
[10] On Isodual Cyclic Codes over Finite Chain Rings
Batoul, Aicha
Guenda, Kenza
Gulliver, T. Aaron
Aydin, Nuh
CODES, CRYPTOLOGY AND INFORMATION SECURITY, C2SI 2017, 2017, 10194 : 176 - 194

← 1 2 3 4 5 →