Do non-free LCD codes over finite commutative Frobenius rings exist?

被引：30

作者：

Bhowmick, Sanjit ^{[1
]}

Fotue-Tabue, Alexandre ^{[2
]}

Martinez-Moro, Edgar ^{[3
]}

Bandi, Ramakrishna ^{[4
]}

Bagchi, Satya ^{[1
]}

机构：

[1] Natl Inst Technol Durgapur, Dept Math, Durgapur, India

[2] Univ Ngaoundere, Dept Math, HTTC Bertoua, Yaounde, Cameroon

[3] Univ Valladolid, Inst Math, Valladolid, Spain

[4] Dr SPM Int Inst Informat Technol, Dept Math, Naya Raipur, India

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2020年 / 88卷 / 05期

关键词：

Frobenius ring; Linear complementary dual code; Constacyclic code; Chain ring; LINEAR CODES; CYCLIC CODES;

D O I：

10.1007/s10623-019-00713-x

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we clarify some aspects of LCD codes in the literature. We first prove that non-free LCD codes do not exist over finite commutative Frobenius local rings. We then obtain a necessary and sufficient condition for the existence of LCD codes over a finite commutative Frobenius ring. We later show that a free constacyclic code over a finite chain ring is an LCD code if and only if it is reversible, and also provide a necessary and sufficient condition for a constacyclic code to be reversible. We illustrate the minimum Lee distance of LCD codes over some finite commutative chain rings with examples. We found some new optimal cyclic codes over Z4of different lengths which are LCD codes using computer algebra system MAGMA.

引用

页码：825 / 840

页数：16

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