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arXiv · 1807.01246

The Concatenated Structure of Quasi-Abelian Codes

Martino Borello·Cem Güneri·Elif Saçıkara·Patrick Solé
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Abstract

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, Sol\'e, (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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Martino Borello, Cem Güneri, Elif Saçıkara, Patrick Solé. 2018-07-03. The Concatenated Structure of Quasi-Abelian Codes. https://arxiv.org/abs/1807.01246

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