Product Codes

Notes

• The hypergraph product is defined in "J. Tillich, G. Zémor. Quantum LDPC codes with positive rate and minimum distance proportional to n^(1/2). (2013) arXiv:0903.0566v2"
• The generalized Shor code is defined in "D. Bacon and A. Casaccino. Quantum error correcting subsystem codes from two classical linear codes. (2006) http://arxiv.org/abs/quant-ph/0610088"
• Hyperbicycle codes are found in "Quantum ``hyperbicycle'' low-density parity check codes with finite rate" and "Quantum Kronecker sum-product low-density parity-check codes with finite rate".
• Generealized bicycle codes are are found in "Quantum ``hyperbicycle'' low-density parity check codes with finite rate", "Quantum kronecker sum-product low-density parity- check codes with finite rate", and "Degenerate Quantum LDPC Codes With Good Finite Length Performance".
• The generalized hypergraph product is defined in "Degenerate Quantum LDPC Codes With Good Finite Length Performance".
• The bias-tailored lifted product is defined in "Bias-tailored quantum LDPC codes".