Construction of quasi-twisted codes and enumeration of defining polynomials

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 and some results are known for larger fields. Quasi-twisted codes are constructed using m × m twistulant matrices and many of these are the best known codes. In this paper, the number of m × m twistulant matrices over Fq is enumerated and linear codes over F17 and F19 are constructed for k up to 5.