Quadratic residue codes over Fp + νFp and their Gray images

Abstract

In this paper quadratic residue codes over the ring F-p + vF(p) are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes enjoy similar properties as quadratic residue codes over finite fields. For the case p = 2, Euclidean and Hermitian self-dual families of codes as extended quadratic residue codes are considered and two optimal Hermitian self-dual codes are obtained as examples. Moreover, a substantial number of good p-ary codes are obtained as images of quadratic residue codes over F-p + vF(p) in the cases where p is an odd prime. These results are presented in tables. (C) 2014 Elsevier B.V. All rights reserved.