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# Double circulant and quasi-twisted self-dual codes over $\mathbb F_5$ and $\mathbb F_7$

• In this paper, we consider double circulant and quasi-twisted selfdual codes over $\mathbb F_5$ and $\mathbb F_7$. We determine the highest minimum weights for such codes of lengths up to 34 for $\mathbb F_5$ and up to 28 for $\mathbb F_7$, and classify the codes with these minimum weights. In particular, we give a double circulant self-dual [32, 16] code over $\mathbb F_5$ which has a higher minimum weight than the previously best known linear code with these parameters. In addition, a self-dual code over $\mathbb F_7$ is presented which has a higher minimum weight than the previously best known self-dual code for length 28.
Mathematics Subject Classification: 94B05.

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