Group Codes Over Dihedral Group Algebras š¯”½ q [ D 16 ] and š¯”½ q [ Z 2 Ć— D 8 ]
Zhihao Tian, Yanyan Gao Ā· Journal of Mathematics Ā· 2025
Let denote a finite field of characteristic p , where q = p k for some prime p and integer k . Let D n represent a dihedral group of order n . In this paper, group codes in the dihedral group algebras and are proposed. We compute the unique (both linear and nonlinear) idempotents of 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 and .