Construction of quasi-twisted codes and enumeration of defining polynomials
DOI:
https://doi.org/10.13069/jacodesmath.645015Keywords:
Finite fields, Twistulant matrices, Quasi-twisted codes, Optimal codes, Griesmer boundAbstract
Let $d_{q}(n,k)$ be the maximum possible minimum Hamming distance of a linear [$n,k$] code over $\mathbb{F}_{q}$. 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 $\mathbb{F}_q$ is enumerated and linear codes over $\mathbb{F}_{17}$ and $\mathbb{F}_{19}$ are constructed for $k$ up to $5$.
Received: 27 June 2019 | Accepted: 20 September 2019Downloads
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