Relationship between Codes and Idempotents in a Dihedral Group Algebra

被引：1

作者：

Vedenev, K. V. ^{[1
]}

Deundyak, V. M. ^{[1
,2
]}

机构：

[1] Southern Fed Univ, Rostov Na Donu 344006, Russia

[2] State Sci Org Res Inst Spetsvuzavtomatika, Rostov Na Donu 344002, Russia

来源：

MATHEMATICAL NOTES | 2020年 / 107卷 / 1-2期

关键词：

dihedral group; group algebras; idempotents; Wedderburn decomposition; non-commutative codes;

D O I：

10.1134/S0001434620010204

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Codes in the dihedral group algebra FqD2n, i.e., left ideals in this algebra, are studied. A generating idempotent is constructed for every code in FqD2n given by its image under the Wedderburn decomposition of this algebra. By using a selected set of idempotents, the inverse Wedderburn transform for the algebra FqD2n is constructed. The image of some codes under the Wedderburn decomposition is described directly in terms of their generating idempotents. Examples of the application of the obtained results to induced codes are considered.

引用

页码：201 / 216

页数：16

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