Lean 4 kernel check of A(32,8,8) ≥ 1713 for QH-Lin's constant-weight code

Lean 4 kernel check (decide +kernel, no native_decide, Lean core only) that QH-Lin's 1713 binary words of length 32 have weight 8 and pairwise Hamming distance at least 8, i.e. A(32,8,8) ≥ 1713, in two separate encodings. Theorem Kern32_8_8.A_32_8_8_ge_1713, axioms [propext, Classical.choice, Quot.sound]. The code is QH-Lin's (github.com/QH-Lin/kissing-number-32, commit f367a9c5); this upload only checks it. The step to the kissing configuration is cited, not formalised. Lean sources, generators and checksums are in certificates_A32_8_8.zip. Version 2: the encoding-2 theorem now states M = 1713 together with the weight and pair conditions, in bit-clearing form, for every index below M; axioms unchanged. The popcount form is proved for encoding 1.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23872565
Primary Topic
Coding theory and cryptography
Type
preprint
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preprint

Lean 4 kernel check of A(32,8,8) ≥ 1713 for QH-Lin's constant-weight code

Advatiya Thalluri
1 links
Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
preprint

Lean 4 kernel check of A(32,8,8) ≥ 1713 for QH-Lin's constant-weight code

Advatiya Thalluri
preprint en

Abstract

Lean 4 kernel check (decide +kernel, no native_decide, Lean core only) that QH-Lin's 1713 binary words of length 32 have weight 8 and pairwise Hamming distance at least 8, i.e. A(32,8,8) ≥ 1713, in two separate encodings. Theorem Kern32_8_8.A_32_8_8_ge_1713, axioms [propext, Classical.choice, Quot.sound]. The code is QH-Lin's (github.com/QH-Lin/kissing-number-32, commit f367a9c5); this upload only checks it. The step to the kissing configuration is cited, not formalised. Lean sources, generators and checksums are in certificates_A32_8_8.zip. Version 2: the encoding-2 theorem now states M = 1713 together with the weight and pair conditions, in bit-clearing form, for every index below M; axioms unchanged. The popcount form is proved for encoding 1.

Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
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