On the Linear Codes Over the Ring Rp

Abstract

Some results are generalized on linear codes over Z(3)[v]/< v(3) - v > in [15] to the ring R-p = Z(p)[v]/< v(p) - v >, where p is an odd prime number. The Gray images of cyclic and quasi-cyclic codes over R-p are obtained. The parameters of quantum error correcting codes are obtained from negacyclic codes over R-p. A nontrivial automorphism theta(p) on the ring R-p is determined. By using this, the skew cyclic, skew quasi-cyclic, skew constacyclic codes over R-p are introduced. The number of distinct skew cyclic codes over R-p is given. The Gray images of skew codes over R-p are obtained. The quasi-constacyclic and skew quasi-constacyclic codes over R-p are introduced. MacWilliams identities of linear codes over R-p are given.