Quantum codes from cyclic codes over the ring Fq+v1Fq++vrFq

Let R=Fq+v1Fq++vrFq, where q is a power of a prime, vi2 0 for 1i,jr and r1. In this paper, the structure of cyclic codes over the ring R is studied and a Gray map phi from Rn to Fq(r+1)n is given. We give a construction of quantum codes from cyclic codes over the ring R. We derive Euclidean dual containing codes over Fq and Hermitian dual containing codes over Fp2m as Gray images of cyclic codes over R. In particular, we use r+1 codes associated with a cyclic code over R of arbitrary length to determine the parameters of the corresponding quantum code. Furthermore, some new non-binary quantum codes are obtained.