A CSS construction embeds qLDPC codes to produce 4D and 5D layer codes with parameters that saturate the BPT bounds and preserve energy barrier scaling.
However, due to the 5D hypercube structure (3D grid structure of qubits), the strings are somewhat more complicated, even more so than the 4D case
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4D and 5D Layer Codes through Color Routing
A CSS construction embeds qLDPC codes to produce 4D and 5D layer codes with parameters that saturate the BPT bounds and preserve energy barrier scaling.