Reed-Muller codes achieve the full achievable rate region on two-user additive-noise channels, and the resulting quantum CSS codes meet the hashing bound across a continuous range of Pauli noise parameters.
Quantum Reed-Muller Codes
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abstract
A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]] = [[2^r, 2^r - C(r,t) - 2 sum_{i=0}^{t-1} C(r,i), 2^t + 2^{t-1} ]].
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Reed-Muller Codes for Quantum Pauli and Multiple Access Channels
Reed-Muller codes achieve the full achievable rate region on two-user additive-noise channels, and the resulting quantum CSS codes meet the hashing bound across a continuous range of Pauli noise parameters.