Clifford Code Constructions of Operator Quantum Error Correcting Codes
arXiv:quant-ph/0604161
Abstract
Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in terms of Clifford codes, an elegant generalization of stabilizer codes due to Knill. Character-theoretic methods are used to derive a simple method to construct operator quantum error-correcting codes from any classical additive code over a finite field.
11 pages of character theory; minor changes, theorem 6 added