Preprint
Sep 2026
There Are No Nontrivial Perfect Codes in the Johnson Scheme
In his seminal work from 1973, Delsarte conjectured that the Johnson schemes admit no nontrivial perfect codes. We prove this fundamental conjecture which is central in combinatorial coding theory. Our arguments combine lower bounds on the design strength of a perfect code with divisibility conditions for the size of a...
T. Etzion, Xian-De Zhang, Wen-Jie Zhong
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