On LCD, self dual and isodual cyclic codes over finite chain rings

被引：1
作者：
Benyettou, Amel [1 ]
Batoul, Aicha [1 ]
Fernandez-Cordoba, Cristina [2 ]
机构：
[1] Univ Sci & Technol Algiers Algeria, Fac Math USTHB, Bab Ezzouar, Algeria
[2] Univ Autonomous Barcelona, Dept Informat & Commun Engn, Barcelona, Spain
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2022年 / 79卷
关键词：
LCD; Isodual; Self dual; Cyclic codes; Finite chain rings;
D O I：
10.1016/j.ffa.2022.101993
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, LCD cyclic, self dual and isodual codes over finite chain rings are investigated. It was proven recently that a non-free LCD cyclic code does not exist over finite chain rings. Based on algebraic number theory, we introduce necessary and sufficient conditions for which all free cyclic codes over a finite chain ring are LCD. We have also obtained conditions on the existence of non trivial self dual cyclic codes of any length when the nilpotency index of the maximal ideal of a finite chain ring is even. Further, several constructions of isodual codes are given based on the factorization of the polynomial x(n) - 1 over a finite chain ring. (C) 2022 The Author(s). Published by Elsevier Inc.
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页数：25
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