Abstract: The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding classical self-orthogonal linear codes over the Galois field GF(4) under a Hermitian inner product. A classical cyclic code over the field GF(4) is self-orthogonal with respect to the Hermitian inner product iff the generator polynomial of its dual code is a factor of its generator polynomial. Based on this connection, a class of quantum cyclic codes is constructed by finding corresponding classical cyclic codes. Some examples are also given in detail.

Key words: quantum cyclic codes, stabilizer quantum-error-correcting codes, cyclic codes over the field GF(4), Hermitian inner product, self-orthogonal