准阿贝尔码的级联结构
The Concatenated Structure of Quasi-Abelian Codes
摘要：
在（Jitman，Ling，（2015））中给出了将准阿贝尔码分解为更大字母表上的更短线性码，扩展了类似的准循环码的中国余数分解（Ling，Solé，（2001））。我们给出了一个级联分解的准阿贝尔码，并显示，在准循环的情况下，这两个分解是等价的。级联分解使我们能够给出准阿贝尔码的一般最小距离界，并构造出一些最优码。此外，我们通过例子表明，在某些情况下，最小距离界是尖锐的。此外，还给出了约半速率的大型严格准阿贝尔码的例子。级联结构也使我们能够得出结论，严格准阿贝尔线性互补对偶码在任何有限域上是渐近好的。
英文摘要：
The decomposition of a quasi-abelian code into shorter linear codes over larger alphabets was given in (Jitman, Ling, (2015)), extending the analogous Chinese remainder decomposition of quasi-cyclic codes (Ling, Solé, (2001)). We give a concatenated decomposition of quasi-abelian codes and show, as in the quasi-cyclic case, that the two decompositions are equivalent. The concatenated decomposition allows us to give a general minimum distance bound for quasi-abelian codes and to construct some optimal codes. Moreover, we show by examples that the minimum distance bound is sharp in some cases. In addition, examples of large strictly quasi-abelian codes of about a half rate are given. The concatenated structure also enables us to conclude that strictly quasi-abelian linear complementary dual codes over any finite field are asymptotically good.
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