Abstract: A new class of quantum stabilizer codes is presented. The problem of finding stabilizer quantum-error-correcting codes can be transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Based on this connection, one method for constructing quantum constacyclic codes is presented by finding self-orthogonal classical constacyclic codes over the field GF(4) under a trace inner product. Finally, some examples are given. As an application of this method, quantum Hamming codes are constructed. This class of quantum codes includes well-known quantum cyclic codes.

Key words: quantum constacyclic codes, stabilizer quantum-error-correcting codes, constacyclic codes over GF(4), quantum Hamming codes