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arXiv · 2609.23368

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

Xiande Zhang·Wenjie Zhong
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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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Xiande Zhang, Wenjie Zhong. 2026-09-20. The Last Seven Open Radii for Perfect Codes in the Johnson Scheme. https://arxiv.org/abs/2609.23368

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