Self-dual 2-quasi-abelian Codes

08/17/2021

∙

by   Liren Lin, et al.

∙

0

∙

share

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.