Framework
Adinkra Error Correction
Doubly-even codes provide structural stability and noise resilience across the hypercube
Error Correction Bound
A linear code with minimum distance d corrects all error patterns of weight t when:
2t < d
If codeword c receives error e (weight t) giving r = c ⊕ e, then c is the unique nearest codeword to r. Nearest-neighbor decoding succeeds.
Simulation Verification
Total variation distance stays below 0.05 for perturbation rates up to 6%, matching the theoretical Hamming bound. The embedded codes provide genuine structural protection.
Adinkra Graph Origins
Adinkra graphs (Faux & Gates 2005) encode supersymmetry multiplet relationships. The doubly-even property emerges from the algebraic requirement that SUSY transformations square to translations, constraining codeword weights to multiples of 4.