The Last Seven Open Radii for Perfect Codes in the Johnson Scheme

Xiande Zhang, Wenjie Zhong

Source record

Source: arXiv

Published: Sep 20, 2026

arXiv: 2609.23368

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Source abstract

Delsarte (1973) conjectured that there are no nontrivial perfect codes in the Johnson scheme. In this paper, we prove that there are no nontrivial $e$ -perfect codes in the Johnson scheme for $e\in\{1,2,4,9,10,12,16\}$ . This paper complements "Perfect Codes in the Johnson Scheme Hardly Exist", thus proving Delsarte's conjecture completely.

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The Last Seven Open Radii for Perfect Codes in the Johnson Scheme — Mathematical Frontier Network