Self-dual $2$-quasi-abelian Codes

Liren Lin; Yun Fan

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arXiv · 2108.07427

Self-dual $2$-quasi-abelian Codes

Liren Lin·Yun Fan

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Abstract

A kind of self-dual quasi-abelian codes of index $2$ over any finite field $F$ is introduced. By counting the number of such codes and the number of the codes of this kind whose relative minimum weights are small, such codes are proved to be asymptotically good provided $-1$ is a square in $F$. Moreover, a kind of self-orthogonal quasi-abelian codes of index $2$ are defined; and such codes always exist. In a way similar to that for self-dual quasi-abelian codes of index $2$, it is proved that the kind of the self-orthogonal quasi-abelian codes of index $2$ is asymptotically good.

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Liren Lin, Yun Fan. 2021-08-17. Self-dual $2$-quasi-abelian Codes. https://arxiv.org/abs/2108.07427

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