On self-dual double circulant codes

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Alahmadi, Adel and Özdemir, Funda and Patrick, Solé (2017) On self-dual double circulant codes. Designs, Codes, and Cryptography . ISSN 0925-1022 (Print) 1573-7586 (Online) Published Online First http://dx.doi.org/10.1007/s10623-017-0393-x

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Official URL: http://dx.doi.org/10.1007/s10623-017-0393-x


Self-dual double circulant codes of odd dimension are shown to be dihedral in even characteristic and consta-dihedral in odd characteristic. Exact counting formulae are derived for them, generalizing some old results of MacWilliams on the enumeration of circulant orthogonal matrices. These formulae, in turn, are instrumental in deriving a Varshamov–Gilbert bound on the relative minimum distance of this family of codes.

Item Type:Article
Uncontrolled Keywords:Quasi-cyclic codes, Dihedral group, Consta-dihedral codes, Artin primitive root conjecture
Subjects:Q Science > QA Mathematics > QA150-272.5 Algebra
ID Code:29308
Deposited By:Funda Özdemir
Deposited On:09 Sep 2017 21:54
Last Modified:03 Sep 2019 14:44

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