What this is
The Leech lattice is the unique even unimodular lattice in 24 dimensions with no vectors of norm 2. It holds the record for the densest known sphere packing in 24 dimensions (also Viazovska et al., 2022). Our codec builds the Leech lattice from the extended binary Golay code [24,12,8], the same construction Conway and Sloane formalized. The 196,560 minimal vectors fall into three families (type 2, 3, 4 in the standard classification), and our implementation enumerates and verifies all of them.
Why it matters
The Leech lattice underpins some of the most efficient known error-correcting codes and appears in theoretical proposals for post-quantum primitives. More directly: being able to enumerate and verify the kissing number of a 24-dimensional lattice is a capability statement. It demonstrates that our lattice geometry work is not superficial. The Golay construction also connects directly to quantum error correction (the perfect binary Golay code is used in some QEC schemes).
Technical Specification
- -Dimension: 24
- -Base code: binary Golay [24,12,8], minimum distance 8 verified
- -Kissing number: 196,560, all three vector families enumerated
- -Construction: Conway-Sloane MOG (Miracle Octad Generator)
- -Minimal vector norms: type 2, 3, 4 all verified
- -Status: internal, not published; IP Claim filed