Construction of s-extremal optimal unimodular lattices in dimension 52

Abstract

An s-extremal optimal unimodular lattice in dimension 52 is constructed for the first time. This lattice is constructed from a certain self-dual ${\mathbb{F}}_5$-code by Construction A. In addition, as neighbours of the lattice, two more s-extremal optimal unimodular lattices are constructed.

Keywords:

• Unimodular lattice
• self-dual code
• Construction A
• s-extremal unimodular lattice
• optimal lattice

2010 Mathematics Subject Classifications:

• 11H06
• 11H71
• 94B75

Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 19H01802.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by JSPS KAKENHI [grant number 19H01802].