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≥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.
Barg, A., Glazyrin, A., Kao, W. J., Lai, C. Y., Tseng, P. C., & Yu, W. H. (2022). On the size of maximal binary codes with 2, 3, and 4 distances. arXiv preprint arXiv:2210.07496.
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