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This paper investigated quadratic residue codes over Fp + uFp + vFp + uvFp, where u² = u, v² = v, uv = vu and p is odd prime. At first, it introduced the basic knowledge of cyclic codes of length n over Fp + uFp + vFp + uvFp, then obtained the structures of quadratic residue codes over Fp + uFp + vFp + uvFp by applying their generating idempotents, and discussed the relations and dual properties between these codes and their extended codes. Finally, it gave the specific forms of generating idempotents of quadratic residue codes of length 11 over the ring F3 + uF3 + vF3 + uvF3 . [ABSTRACT FROM AUTHOR]

This paper investigated quadratic residue codes over Fp + uFp + vFp + uvFp, where u² = u, v² = v, uv = vu and p is odd prime. At first, it introduced the basic knowledge of cyclic codes of length n over Fp + uFp + vFp + uvFp, then obtained the structures of quadratic residue codes over Fp + uFp + vFp + uvFp by applying their generating idempotents, and discussed the relations and dual properties between these codes and their extended codes. Finally, it gave the specific forms of generating idempotents of quadratic residue codes of length 11 over the ring F3 + uF3 + vF3 + uvF3 . [ABSTRACT FROM AUTHOR]