A machine-checked proof of the Dong-Yang classification of optimal (n,4) binary codes for BSCs

2026-09-05

AI Summary

使用AI工具辅助Lean 4形式化验证Dong和Yang关于最优(n,4)二进制码分类的证明，修正了原论文中的错误并简化了证明。

Abstract

We present a machine-checked Lean~4 formalization of Dong and Yang's classification of optimal finite-length $(n,4)$ binary block codes for binary symmetric channels. The formalization was developed mainly by feeding the paper's proofs to an AI tool. To establish correctness, the authors verified the main theorem statements in Lean and the accepted axioms. This note discusses the corrections and simplifications made to the AI-generated formalization, and records discrepancies found in the paper during the formalization. The Lean code is available at https://github.com/shhyang/n4code_lean.

Problem

• binary symmetric channels
• optimal (n,4) binary codes
• formal verification

Innovation

• machine-checked proof
• AI tool
• formalization
• binary symmetric channels
• Lean 4