A new look at the Golay (23, 12) code (Corresp.)

The (23, 12) binary Golay code is a member of a class of linear codes, obtained by extending nonlinear double-error-correcting codes recently discovered. While all other codes of the class have minimum distance
d_m
= 6, the (23, 12) code owes its unique property (
d_m
= 7) to the nonexistence of the BCH code of length 7 and
d_m
= 6.