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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2020 Volume 107, Issue 2, Pages 178–194 (Mi mzm12194)

This article is cited in 1 paper

Relationship between Codes and Idempotents in a Dihedral Group Algebra

K. V. Vedeneva, V. M. Deundyakba

a Southern Federal University, Rostov-on-Don
b State Scientific Organization: Research Institute "Spetsvuzavtomatika", Rostov-on-Don

Abstract: Codes in the dihedral group algebra $\mathbb{F}_qD_{2n}$, i.e., left ideals in this algebra, are studied. A generating idempotent is constructed for every code in $\mathbb{F}_qD_{2n}$ 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 $\mathbb{F}_qD_{2n}$ 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.

Keywords: dihedral group, group algebras, idempotents, Wedderburn decomposition, noncommutative codes.

UDC: 519.7

Received: 17.09.2018

DOI: 10.4213/mzm12194


 English version:
Mathematical Notes, 2020, 107:2, 201–216

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© Steklov Math. Inst. of RAS, 2025