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.
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Received: 25 July 2006
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Gaborit, P. A bound for certain s-extremal lattices and codes. Arch. Math. 89, 143–151 (2007). https://doi.org/10.1007/s00013-006-1164-5
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DOI: https://doi.org/10.1007/s00013-006-1164-5