The concatenated structure of quasi-abelian codes

Borello, Martino and Güneri, Cem and Saçıkara, Elif and Solé, Patrick (2022) The concatenated structure of quasi-abelian codes. Designs, Codes, and Cryptography, 90 (11). pp. 2647-2661. ISSN 0925-1022 (Print) 1573-7586 (Online)

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The decomposition of a quasi-abelian code into shorter linear codes over larger alphabets was given in Jitman and Ling (Des Codes Cryptogr 74:511–531, 2015), extending the analogous Chinese remainder decomposition of quasi-cyclic codes (Ling and Solé in IEEE Trans Inf Theory 47:2751–2760, 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.
Item Type: Article
Uncontrolled Keywords: Additive abelian codes; Concatenated codes; Linear complementary dual codes; Optimal codes; Quasi-abelian codes
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Cem Güneri
Date Deposited: 05 Sep 2023 11:34
Last Modified: 05 Sep 2023 11:34

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