Hadamard Matrices
Walsh functions · Fast Hadamard transform · Error-correcting codes
Order n = 2^k, k:
4
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Matrix
Walsh Funcs
FHT
Error Codes
Selected row:
0
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H_n = H_1 ⊗ H_{n/2}
— Sylvester construction
Key property:
H·Hᵀ = n·I — rows are orthogonal with equal norm.
FHT:
O(n log n) transform — "Hadamard FFT"
ECC:
First-order Reed-Muller code corrects up to (n/2−1) errors.