Perfect single error-correcting codes in the Johnson Scheme

Details Perfect single error-correcting codes in the Johnson Scheme Perfect single error-correcting codes in the Johnson Scheme

2005-08-29

arxiv.org/abs/math/0508575v2

Mathematics

Combinatorics

4 pages, revised, accepted for publication in IEEE Transactions on Information Theory

Scientific paper

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.

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