, Volume 89, Issue 2, pp 143-151,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 04 Apr 2007

A bound for certain s-extremal lattices and codes

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.

Received: 25 July 2006