Remarkable Degenerate Quantum Stabilizer Codes Derived from Duadic Codes

Abstract

Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand, do not require active error correction, but perform poorly in terms of minimum distance. In this paper, examples of degenerate quantum codes are constructed that have better minimum distance than decoherence free subspaces and allow some errors of small weight that do not require active error correction. In particular, two new families of [[n,1,>= sqrt(n)]]_q degenerate quantum codes are derived from classical duadic codes.