On self-dual double circulant codes

Alahmadi, Adel and Özdemir, Funda and Solé, Patrick (2018) On self-dual double circulant codes. Designs, Codes, and Cryptography, 86 (6). pp. 1257-1265. ISSN 0925-1022 (Print) 1573-7586 (Online)

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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: Artin primitive root conjecture; Consta-dihedral codes; Dihedral group; Quasi-cyclic codes
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Funda Özdemir
Date Deposited: 16 May 2023 15:09
Last Modified: 16 May 2023 15:09
URI: https://research.sabanciuniv.edu/id/eprint/45583

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