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math.CO2026
The Last Seven Open Radii for Perfect Codes in the Johnson Scheme
Xiande Zhang, Wenjie Zhong
Delsarte (1973) conjectured that there are no nontrivial perfect codes in the Johnson scheme. In this paper, we prove that there are no nontrivial -perfect codes in the Johnson…
math.CO2026
There Are No Nontrivial Perfect Codes in the Johnson Scheme
Tuvi Etzion, Xiande Zhang, Wenjie Zhong
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 combinatori…