On Optimal Binary One-Error-Correcting Codes of Lengths $2^m-4$ and $2^m-3$

Denis S. Krotov, Patric R. J. Östergård, Olli Pottonen

Best and Brouwer [Discrete Math. 17 (1977), 235-245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length $2^m-4$ and $2^m-3$, respectively) ar…