A Type II lattice of norm 8 in dimension 72
Jean-Claude Belfiore, Patrick Sol\'e
TL;DR
This paper constructs a specific high-dimensional Type II lattice of norm 8 using coding theory and explores its symmetry properties, contributing to the understanding of lattice structures in mathematics.
Contribution
It introduces a new lattice in dimension 72 derived from an extended quadratic residue code over Z8, highlighting its automorphism group structure.
Findings
Constructed a Type II lattice of dimension 72 with norm 8.
Identified a subgroup of automorphisms isomorphic to PSL(2,71).
Advances understanding of lattice symmetries in high dimensions.
Abstract
A Type II lattice of norm 8 in dimension 72 is obtained by Construction A applied to an extended Quadratic Residue code over Z8. Its automorphism group contains a subgroup isomorphic to PSL(2,71).
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Taxonomy
TopicsCoding theory and cryptography · Finite Group Theory Research