Leech lattice
Definition
Definition via a unique characterization
The Leech lattice is the unique lattice in 24-dimensional Euclidean space satisfying all of the following conditions:
| Condition name | What it means |
|---|---|
| unimodular lattice | The lattice can be generated by a set of basis vectors such that the determinant of the matrix formed by these vectors is 1. |
| even lattice | The square of the length of any vector in the lattice is even. |
| unit balls do not intersect | The length of any non-zero vector in the lattice is greater than 2. Equivalently, unit balls centered at the points of the lattice have empty pairwise intersections. |
Definition using the binary Golay code
The Leech lattice can be defined in terms of the binary Golay code.