Perfect single error-correcting codes in the Johnson Scheme
arXiv:math/0508575 · doi:10.1109/TIT.2006.881744
Abstract
Delsarte conjectured in 1973 that there are no nontrivial pefect codes in the Johnson scheme. Etzion and Schwartz recently showed that perfect codes must be k-regular for large k, and used this to show that there are no perfect codes correcting single errors in J(n,w) for n <= 50000. In this paper we show that there are no perfect single error-correcting codes for n <= 2^250.
4 pages, revised, accepted for publication in IEEE Transactions on Information Theory