A new shortening method and Hermitian self-dual codes over F-2 + vF(2)

Abstract

In this paper, we investigate free Hermitian self-dual codes whose generator matrices are of the form [I, A + vB] over the ring F-2 + vF(2) = {0, 1, v, 1 + v} with v(2) = v. We use the double-circulant, the bordered double-circulant and the symmetric construction methods to obtain free Hermitian self-dual codes of even length. By describing a new shortening method over this ring, we are able to obtain Hermitian self-dual codes of odd length. Using these methods, we also obtain a number of extremal codes. We tabulate the Hermitian self-dual codes with the highest minimum weights of lengths up to 50. (C) 2019 Elsevier B.V. All rights reserved.