Optimal binary one-error-correcting codes of length 10 have 72 codewords

The maximum number of codewords in a binary code with length n and minimum distance d is denoted by A(n, d). By construction it is known that A(10, 3)/spl ges/72 and A(11, 3)/spl ges/144. These bounds have long been conjectured to be the exact values. This is here proved by classifying various codes of smaller length and lengthening these using backtracking and isomorphism rejection. There are 562 inequivalent codes attaining A(10, 3)=72 and 7398 inequivalent codes attaining A(11, 3)=144.