Abstract
Let dq(n,k) be the maximum possible minimum Hamming distance of a linear [n,k] code over Fq. Tables of best known linear codes exist for small fields. In this paper, linear codes over F13 are constructed for k up to 6. The codes constructed are from the class of quasi-cyclic codes. The number of m×m circulant matrices over Fq is enumerated. In addition, the minimum distance of the extended quadratic residue code of length 44 is determined.
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