On self-dual double negacirculant codes
Adel Alahmadi, Hatoon Shohaib, Patrick Sol\'e
TL;DR
This paper investigates self-dual double negacirculant codes, revealing their dihedral structure, deriving counting formulas, and analyzing codes of length a power of two with favorable distance properties.
Contribution
It introduces the dihedral nature of self-dual DN codes, provides exact enumeration formulas, and studies length power-of-two codes using Dickson polynomials.
Findings
Self-dual DN codes are consta-dihedral.
Derived exact counting formulas for DN codes.
Identified code families with distances meeting a modified Gilbert-Varshamov bound.
Abstract
Double negacirculant (DN) codes are the analogues in odd characteristic of double circulant codes. Self-dual DN codes of odd dimension are shown to be consta-dihedral. 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 Gilbert-Varshamov bound.
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