New minimum-distance bounds for generalized bicycle codes are used to construct two degree-4 check families, [[d^2+1,2,d]] and [[d^2,2,d]], with surface-code-comparable simulated thresholds and a logical CNOT via relabeling.
Degenerate quantum LDPC codes with good finite length performance
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Generalized Bicycle Codes with Low Connectivity: Minimum Distance Bounds and Hook Errors
New minimum-distance bounds for generalized bicycle codes are used to construct two degree-4 check families, [[d^2+1,2,d]] and [[d^2,2,d]], with surface-code-comparable simulated thresholds and a logical CNOT via relabeling.