 Syndrome classification of code cosets

For a rank-$(N-k)$ parity-check matrix of a linear code $C$, two words have equal syndromes exactly when their difference lies in $C$. Thus attainable syndromes label cosets bijectively. For a received word $c+e$, its syndrome is that of the error $e$, so minimum-weight representatives provide minimum-distance decoding.

// Target: algebra.bigb