The covering radius of the Leech lattice

1982/04/08 by John H. Conway, Richard Parker, N. J. A. Sloane · 5 citations
Computer Science · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #Advanced Algebra and Geometry #Leech #Unimodular matrix #Lattice (music) #Hexagonal lattice #Combinatorics #Physics #Mathematics #Reciprocal lattice #Geometry #Condensed matter physics #Computer science #Quantum mechanics

paper · doi:10.1098/rspa.1982.0042

openalex publication_date 1982/04/08 · openalex created_date 2022/05/12 · openalex updated_date 2026/07/28

Abstract

Abstract We investigate the points in 24-dimensional space at maximum distance from the Leech lattice, i. e. the ‘deepest holes’ in that lattice. The maximum distance of any such point from the Leech lattice is shown to be 1/√2 times the minimum distance between the lattice points. Furthermore there are 23 types of ‘deepest hole’, one for each of the 23 even unimodular 24-dimensional lattices found by Niemeier.

Cited by

• The automorphism group of the 26-dimensional even unimodular Lorentzian lattice
• The maximal subgroups of Conway's group Co1
• Twenty-three constructions for the Leech lattice
• Geometric generators for braid-like groups
• Leech lattice [wikipedia]