A class of self-dual quasi-abelian codes of index 2 over any finite field FF 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 FF . 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.

中文翻译：

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自对偶 2-拟阿贝尔码


引入一类在任意有限域FF上下标为2的自对偶准阿贝尔码。通过计算此类代码的数量以及此类中相对最小权重较小的代码的数量，只要-1是FF中的平方，则证明此类代码是渐近良好的。此外，还定义了一类索引为2的自正交拟阿贝尔码；并且这样的代码总是存在的。以类似于指数为2的自对偶拟交换码的方式，证明了这些指数为2的自正交拟交换码是渐近好的。