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Perfect single error-correcting codes in the Johnson Scheme

Daniel M. Gordon
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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.

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Daniel M. Gordon. 2006-07-05. Perfect single error-correcting codes in the Johnson Scheme. https://doi.org/10.1109/tit.2006.881744

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