Quadratic Residue Codes over F_p + vF_p + v~2F_p

摘要

This article studies quadratic residue codes of prime length q over the ring R = F_p + vF_p + v~2F_p, 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 F_7 and F_(13) are constructed.