Problem
Research questions and friction points this paper is trying to address.
Perfect Codes
Johnson Scheme
Delsarte's Conjecture
The Last Seven Open Radii for Perfect Codes in the Johnson Scheme
🤖 AI Summary
本文解决了Delsarte关于Johnson方案中不存在非平凡完美码的猜想，通过证明当e属于{1,2,4,9,10,12,16}时，不存在非平凡e-完美码。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
perfect codes
Johnson scheme
Delsarte's conjecture
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