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 self-orthogonal codes over the Galois field GF(4) under a trace inner product. Based on this connection, the necessary and sufficient condition is proved under which classical convolutional codes over GF(4) are self-orthogonal with respect to the trace inner product, and then corresponding codes satisfying the condition are found. Tail-biting codes with a simple block structure are obtained by “tail-biting” transformation, which are self-orthogonal with respect to the trace inner product. Finally, relative quantum stabilizer codes are constructed. The code construction is simple, and the minimum distance of the code approaches the upper bound.

Key words: stabilizer quantum-error-correcting codes, classical convolutional codes, tail-biting codes, trace inner product, self-orthogonal