Parity checks

A parity-check matrix produces a syndrome that diagnoses violations of code constraints.

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Error correction bounds
Minimum distance d permits correcting up to floor((d-1)/2) arbitrary symbol errors.
Linear codes
Codewords forming a finite-field vector subspace enable algebraic encoding and decoding.
Channel capacity
Capacity bounds achievable reliable information rates for a specified channel model.
Conditional entropy
Conditional entropy averages remaining uncertainty after another variable is observed.
Hamming distance
Hamming distance counts differing positions between equal-length strings.