Perfect single error-correcting codes in the Johnson scheme
Daniel M. Gordon · 2008
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≤50,000. In this paper we show that there are no perfect single error-correcting codes for n≤2^250.