The Construction A lattice of the extended binary Golay code #
Construction A applied to the extended binary Golay code produces the rank-24 lattice of
integer vectors in ℚ^(Fin 24) whose reduction modulo two is a Golay codeword, carrying the
halved dot product. Because the Golay code is Type II, doubly even and Euclidean self-dual, this
lattice is positive definite, even, and unimodular.
References #
- W. Ebeling, Lattices and Codes, §§1.3 and 2.8, for Construction A applied to the Golay code.
- J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Chapter 4, §11 and Chapter 7, §6.
The Construction A lattice of the extended binary Golay code: the integer vectors of
ℚ^(Fin 24) reducing to a Golay codeword modulo two, with the dot product halved.
Instances For
The Golay lattice is Construction A applied to the explicit extended binary Golay code.
The Golay Construction A carrier is the lattice of integer lifts of Golay codewords.
The Golay Construction A form is the halved coordinate dot product.
The named Golay Construction A lattice inherits the nondegeneracy of Construction A.
The Golay Construction A lattice has rank 24.
The Golay Construction A lattice is positive definite.
The Golay Construction A lattice is even.
The Golay Construction A lattice is unimodular.