Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.10579

Authors: Yang, Shenghao, Dong, Yanyan

Institutions: Chinese University of Hong Kong, Chinese University of Hong Kong, Shenzhen

Language: English

Topic: Coding theory and cryptography

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Shenzhen Fundamental Research Program

Awards: G2582247629, G5563798569, G7362582964

OpenAlex ID: W7212311049

Cites: 10

Cited by: 1

Related to: 10