Idempotent generators of cyclic and quadratic residue codes over F3 + vF3

Abstract EN

In this paper we study idempotent generators of cyclic codes and quadratic residue codes over R = F3 + vF3, where v2 = 1 and F3 = f0; 1 ; 2g.

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 extended 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 ascertained.