Group Codes Over Dihedral Group Algebras 𠔽q[D16] and 𠔽q[Z2 × D8]

Zhihao Tian and Yanyan Gao

Journal of Mathematics, 2025, vol. 2025, 1-12

Abstract: Let Fq denote a finite field of characteristic p, where q=pk for some prime p and integer k. Let Dn represent a dihedral group of order n. In this paper, group codes in the dihedral group algebras FqD16 and FqZ2×D8 are proposed. We compute the unique (both linear and nonlinear) idempotents of FqDn corresponding to the characters of dihedral groups and utilize these results to characterize the minimum distances and dimensions of the resulting group codes. Moreover, we construct maximum distance separable (MDS) group codes and almost MDS group codes in FqD16 and FqZ2×D8.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7629466

DOI: 10.1155/jom/7629466

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