Quasi-cyclic codes over F13F13 and enumeration of defining polynomials

Let dq(n,k)dq(n,k) be the maximum possible minimum Hamming distance of a linear [n,kn,k] code over FqFq. Tables of best known linear codes exist for small fields. In this paper, linear codes over F13F13 are constructed for k   up to 6. The codes constructed are from the class of quasi-cyclic codes. The number of m×mm×m circulant matrices over FqFq is enumerated. In addition, the minimum distance of the extended quadratic residue code of length 44 is determined.