Archiv der Mathematik

, Volume 89, Issue 2, pp 143–151

A bound for certain s-extremal lattices and codes

Authors

Open AccessArticle

DOI: 10.1007/s00013-006-1164-5

Cite this article as:
Gaborit, P. Arch. Math. (2007) 89: 143. doi:10.1007/s00013-006-1164-5

Abstract.

In this paper we introduce the notion of s-extremal lattice for unimodular Type I lattices. We give a bound on the existence of certain such s-extremal lattices: an s-extremal lattice of dimension n and minimal even norm μ must satisfy n < 12μ. This result implies that such lattices are also extremal and that there are a finite number of them. We also give an equivalent bound for s-extremal self-dual codes: an s-extremal code with doubly-even minimum distance d and length n must satisfy n < 6d, moreover such codes are extremal.

Mathematics Subject Classification (2000).

20J05

Keywords.

Unimodular lattices self-dual codes modular forms classification shadow

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007