Constructing error-correcting binary codes using transitive permutation groups

Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error-correcting codes, groups are here considered that act transitively on the pairs of coordinates and coordinate values. By considering such groups in an exhaustive manner and carrying out computer searches, the following new bounds are obtained on A2(n,d), the maximum size of a binary code of length n and minimum distance d: A2(17,3)≥5632, A2(20,3)≥40960, A2(21,3)≥81920, A2(22,3)≥163840, A2(23,3)≥327680, A2(23,9)≥136, and A2(24,5)≥17920.