On self-dual double circulant codes
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
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.
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