Arithmetic of Finite Fields

Abstract

Abstract. This article studies quadratic residue codes of prime length q over the ring R = Fp + vFp + v 2 Fp, where p, q are distinct odd primes. After studying the structure of cyclic codes of length n over R, quadratic residue codes over R are defined by their generating idempotents and their extension codes are discussed. Examples of codes and idempotents for small values of p and q are given. As a by-product almost MDS codes over F7 and F13 are constructed.