On self-dual double negacirculant codes
Alahmadi, Adel and Güneri, Cem and Özkaya, Buket and Shoaib, Hatoon and Sole, Patrick (2017) On self-dual double negacirculant codes. Discrete Applied Mathematics, 222 . pp. 205-212. ISSN 0166-218X (Print) 1872-6771 (Online)
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Official URL: http://dx.doi.org/10.1016/j.dam.2017.01.018
Double negacirculant (DN) codes are the analogues in odd characteristic of double circulant codes. Self-dual DN codes are shown to have a transitive automorphism group. Exact counting formulae are derived for DN codes. The special class of length a power of two is studied by means of Dickson polynomials, and is shown to contain families of codes with relative distances satisfying a modified Varshamov-Gilbert bound. This gives an alternative, and effective proof of the result of Chepyzhov, that there are families of quasi twisted codes above Varshamov-Gilbert.
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