Codes over dihedral groups

Abstract

In this paper we consider the group algebra FG, where characterstic of the field F does not divide order the group G, then FG is semisimple, and hence decomposes into a direct sum of minimal ideals generated by the idempotents .We give the explicit expressions for the idempotents in the group algebra of dihedral group of order 2n for every n. We describe (2n, 2n-1, 2) MDS and (2n, 2n-2, 2) group codes for every n corresponding to the linear idempotents and in case of non linear idempotents Dihedral group codes of length 16, 20,24 are constructed.