Department of Mathematics - Seminar on Applied Mathematics - On the size of maximal binary codes

We address the problems of 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.