Self-dual and LCD double circulant and double negacirculant codes over $${\mathbb {F}}_q+u{\mathbb {F}}_q+v{\mathbb {F}}_q$$

Double circulant self-dual and LCD codes over Galois rings

This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic p and order p with p and odd prime. When p ≡ 3 (mod 4), we give an algorithm to construct a duality preserving bijective Gray map from such a Galois ring to Z p2 . Using random coding, we obtain families of asymptotically good self-dual an...

On self-dual double negacirculant codes

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 Gilb...

Optimal double circulant self-dual codes over 𝔽4 II

On self-dual double circulant codes

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 and used to show they contain families of codes with relative distance satisfying a modified Gilbert-Varshamov bound.

Double and bordered α-circulant self-dual codes over finite commutative chain rings

MICHAEL KIERMAIER, ALFRED WASSERMANN michael.kiermaier, [email protected] Mathematical Department, University of Bayreuth, D-95440 Bayreuth, GERMANY Abstract. In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from α-circulant matrices. For a non-trivial ideal I < R we give a method to lift such codes over R/I to codes over R, ...