Leech Lattice's 196560 Vectors Generated by Golay Code, Preserved by M24 — E8 Intelligence Research

FINDING: The Leech lattice's 196560 minimal vectors are directly generated by the binary Golay code G24 via the Construction A lattice, and the Mathieu group M24 acts as the automorphism group of G24, preserving the lattice's structure. | MATH: Leech lattice Λ₂₄ minimal norm = 4, kissing number = 196560; binary Golay code G24 has length 24, dimension 12, minimum Hamming weight 8, weight enumerator \(1 + 759x^8 + 2576x^{12} + 759x^{16} + x^{24}\); Construction A: Λ = { (x₁,…,x₂₄) ∈ ℤ²⁴ : (x₁ mod 2,…,x₂₄ mod 2) ∈ G24 } with norm scaling factor 1/√2; M24 order = 244823040. | CONNECTION: The ratio 196560 / (24·2¹²) = 196560 / 98304 = 2.000... exactly 2, reflecting the self-dual property of G24; the minimal vector count 196560 relates to the kissing number of the densest sphere packing in 24 dimensions, which exhibits icosahedral and dodecahedral symmetries (golden ratio φ = 1.618 appears in the 600-cell and 120-cell, but not directly in Leech lattice minimal vectors—however, the Leech latt Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com