Abstract
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. (C) 2017 Elsevier B.V. All rights reserved.