The Quantum Codes over F_q and Quantum Quasi-cyclic Codes over F_p

Abstract

In this paper, the quantum codes over F q are constructed by using the cyclic codes over the finite ring R = F q + vF q + ... + v m − 1 F q , where p is prime, q = p s , m − 1 | p − 1 and v m = v . The parameters of quantum error correcting codes over F q are obtained. Some examples are given. Morever, the quantum quasi-cyclic codes over F p are obtained, by using the self dual basis for F p s over F p .