σ-LCD codes over finite chain rings

被引：0

作者：

Liu, Xiusheng ^{[1
]}

Liu, Hualu ^{[2
]}

机构：

[1] Hubei Polytech Univ, Sch Math & Phys, Huangshi 435003, Hubei, Peoples R China

[2] Hubei Univ Technol, Sch Sci, Wuhan 430068, Hubei, Peoples R China

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2020年 / 88卷 / 04期

关键词：

Finite chain ring; Generator matrix; sigma-LCD code; Entanglement-assisted quantum error-correcting code; LINEAR CODES;

D O I：

10.1007/s10623-019-00706-w

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this work, we first generalize the sigma-LCD codes over finite fields to sigma-LCD codes over finite chain rings. Under suitable conditions, linear codes over finite chain rings that are sigma-LCD codes are characterized. Then we provide a necessary and sufficient condition for free constacyclic codes over finite chain rings to be sigma-LCD. We also get some new binary LCD codes of different lengths which come from Gray images of constacyclic sigma-LCD codes over F-2+ gamma F-2+ gamma F-2(2). Finally, for special finite chain rings F-q + gamma F-q, we define a new Gray map Phi from (F-q + gamma F-q)(n) to F-q(2n), and by using sigma--LCD codes over finite chain rings F-q + gamma F-q, we construct new entanglement-assisted quantum error-correcting (abbreviated to EAQEC) codes with maximal entanglement and parts of them are MDS EAQEC codes.

引用

页码：727 / 746

页数：20

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