Skew constacyclic codes over Galois rings

被引：97

作者：

Boucher, Delphine ^{[1
]}

Sole, Patrick ^{[2
]}

Ulmer, Felix ^{[1
]}

机构：

[1] Univ Rennes 1, IRMAR, UMR 6625, F-35042 Rennes, France

[2] I3S, F-06903 Sophia Antipolis, France

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2008年 / 2卷 / 03期

关键词：

cyclic codes; skew polynomial rings; self-dual codes; Z(4)-codes; modular lattices;

D O I：

10.3934/amc.2008.2.273

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We generalize the construction of linear codes via skew polynomial rings by using Galois rings instead of finite fields as coefficients. The resulting non commutative rings are no longer left and right Euclidean. Codes that are principal ideals in quotient rings of skew polynomial rings by a two sided ideals are studied. As an application, skew constacyclic self-dual codes over GR(4, 2) are constructed. Euclidean self-dual codes give self-dual Z(4)-codes. Hermitian self-dual codes yield 3-modular lattices and quasi-cyclic self-dual Z(4)-codes.

引用

页码：273 / 292

页数：20

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