A bound for certain s-extremal lattices and codes
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- Gaborit, P. Arch. Math. (2007) 89: 143. doi:10.1007/s00013-006-1164-5
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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.