Idempotent generators of cyclic and quadratic residue codes over

Abstract

In this paper we study idempotent generators of cyclic codes and quadratic residue codes over R = , where and . The forms of some idempotents over this ring are given, the quadratic residue codes are defined in forms of the idempotent generators, and the relation between them and their ex- tended codes is discussed as well as their duality. The specific forms of idempotent generators of quadratic residue codes of lengths 11 and 13 over the ring R are as-certained. AMS: Mathematics Classification 2010: Primary 94B05, secondary 51E22. Key words: Cyclic codes, Quadratic residue codes, Idempotent generators, dual codes.