Construction of Quasi-Twisted Codes and Enumeration of Defining Polynomials

Let $d_{q}(n,k)$ be the maximum possible minimum Hamming distance of a linear [$n,k$] code over $\F_{q}$. Tables of best known linear codes exist for small fields and some results are known for larger fields. Quasi-twisted codes are constructed using $m \times m$ twistulant matrices and many of these are the best known codes. In this paper, the number of $m \times m$ twistulant matrices over $\FF_q$ is enumerated and linear codes over $\F_{17}$ and $\F_{19}$ are constructed for $k$ up to $5$