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On the size of maximal binary codes with 2, 3, and 4 distances (2210.07496v1)
Published 14 Oct 2022 in math.CO, cs.IT, and math.IT
Abstract: 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.