Self-Dual 2-Quasi Abelian Codes
Liren Lin, Yun Fan · IEEE Transactions on Information Theory · 2022
A class 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 in this class whose relative minimum weights are small, such codes are proved to be asymptotically good provided −1 is a square in$F$. Moreover, a class of self-orthogonal quasi-abelian codes of index 2 is 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 these self-orthogonal quasi-abelian codes of index 2 are asymptotically good.