Enlargement of Calderbank-Shor-Steane quantum codes

It is shown that a classical error correcting code C = [n, k, d] which contains its dual, C⊥ ⊆ C, and which can be enlarged to C ′ = [n, k′ > k + 1, d′], can be converted into a quantum code of parameters [[n, k + k′ − n,min(d, d3d′/2e)]]. This is a generalisation of a previous construction, it enables many new codes of good efficiency to be discovered. Examples based on classical Bose Chaudhuri Hocquenghem (BCH) codes are discussed. keywords Quantum error correction, BCH code, CSS code ∗Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, England.