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Dihedral group codes over finite fields (2001.09402v3)
Published 26 Jan 2020 in cs.IT, math.IT, and math.NT
Abstract: Bazzi and Mitter [3] showed that binary dihedral group codes are asymptotically good. In this paper we prove that the dihedral group codes over any finite field with good mathematical properties are asymptotically good. If the characteristic of the field is even, we construct asymptotically good self-dual dihedral group codes. If the characteristic of the filed is odd, we construct both the asymptotically good self-orthogonal dihedral group codes, and the asymptotically good LCD dihedral group codes.