Quadratic residue codes over Fp+u Fp+ v Fp+uv Fp+v2 Fp+uv2 Fp

Let R=Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp, where u2=1, v3=v, and p is an odd prime. Quadratic residue codes of prime length n=q over the ring R was investigated, where q (q≠p) is an odd prime such that p is a quadratic residue modulo q. The cyclic codes of length n over R were studied, and then the quadratic residue codes over R in terms of idempotent generators were difined. Moreover, the relation between these codes and their extended codes are discussed. Finally, two specific forms of idempotent generators of quadratic residue codes over  Fp+u Fp+v Fp+uv Fp+v2 Fp+uv2 Fp were given to illustrate some results.