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THE CONCATENATED STRUCTURE OF QUASI-ABELIAN CODES

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, 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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https://hal.archives-ouvertes.fr/hal-03346416
Contributor : Patrick Sol'E Connect in order to contact the contributor
Submitted on : Thursday, September 16, 2021 - 12:30:10 PM
Last modification on : Sunday, September 19, 2021 - 3:18:44 AM

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Martino Borello, Cem Güneri, Elif Saçıkara, Patrick Solé. THE CONCATENATED STRUCTURE OF QUASI-ABELIAN CODES. Designs, Codes and Cryptography, Springer Verlag, 2021, ⟨10.1007/s10623-021-00921-4⟩. ⟨hal-03346416⟩

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