Explicit symplectic Barnes-Wall GKP codes achieve rate (1/2) log2 N with constant distance and an exact O(N log^2 N) bounded-distance decoder.
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Symplectic Barnes-Wall GKP Codes: Deterministic $O(N \log^2 N)$ Decoding and Logarithmic Rate Scaling
Explicit symplectic Barnes-Wall GKP codes achieve rate (1/2) log2 N with constant distance and an exact O(N log^2 N) bounded-distance decoder.