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.
翻译:采用某种自体准伙伴指数代码,相对于任何限定字段的美元为2美元,采用某种自体半伙伴指数代码。计算此类代码的数量和相对最低重量小的此类代码的数量,可以证明,此类代码无一例外是好的,只要美元-美元是平方美元。此外,还定义了一种自体准伙伴代码,指数为2美元;这种代码始终存在。以类似于自体准伙伴代码,指数为2美元的方式,证明自体准伙伴代码的指数为2美元。