Galois correspondence on linear codes over finite chain rings

被引：2

作者：

Tabue, Alexandre Fotue ^{[1
]}

Martinez-Moro, Edgar ^{[2
]}

Mouaha, Christophe ^{[3
]}

机构：

[1] Univ Yaounde I, Fac Sci, Dept Math, Yaounde, Cameroon

[2] Univ Valladolid, Inst Math, Castilla, Spain

[3] Univ Yaounde I, Higher Teachers Training Coll Yaounde, Dept Math, Yaounde, Cameroon

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 02期

关键词：

Finite chain rings; Galois correspondence; Galois-subring subcode; CYCLIC CODES;

D O I：

10.1016/j.disc.2019.111653

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S vertical bar T be a Galois extension of finite chain rings and consider H as its group of ring-automorphisms fixing the elements in T. In this paper we determine the stabilizer under such a group of any S-linear code. Using the so called Galois interior a correspondence between subgroups of H and a set of S-linear subcodes of B is determined. Some improvements of upper and lower bounds for the rank of the Galois-subring subcode and trace code are derived from this construction. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：9

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