Abstract
Although it was conjectured by Delsarte in 1973 that no nontrivial perfect codes exist in the Johnson scheme, only very partial results are known. In this paper we considerably reduce the range in which perfect codes in the Johnson scheme can exist; e.g., we show that there are no nontrivial perfect codes in the Johnson graph $J(2w + P,w )$, p prime. We give theorems about the structure of perfect codes if they exist. This involved structure gives more evidence in support of the belief that no nontrivial perfect codes exist in the Johnson scheme.
Full Text 
Sign-in/Register to access full text options
Sign-in/Register to access full text options 
Published version (
Free)
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
