On The Size Of Maximal Binary Codes With 2 3 And 4 Distances

Barg Alexander, Glazyrin Alexey, Kao Wei-jiun, Lai Ching-yi, Tseng Pin-chieh, Yu Wei-hsuan. Arxiv 2022

[Paper]    
ARXIV

We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main results, we determine the exact size of maximal binary codes with two distances for all lengths $n\ge 6$ as well as the exact size of maximal binary constant weight codes with 2,3, and 4 distances for several values of the weight and for all but small lengths.

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