Abstract
Recently there has been tremendous interest in self-dual codes over finite rings, specifically the rings Z/sub 2k/. In this paper, we investigate double circulant self-dual codes over Z/sub 2k/ for small k and short lengths. In particular, we give a classification of the extremal double circulant codes. Using invariant theory, a basis for the space of invariants to which the Hamming weight enumerators belong is given for self-dual codes over Z/sub 6/, Z/sub 8/, Z/sub 10/, and Z/sub 12/.
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