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.