Lattices and codes with long shadows

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Lattices and codes with long shadows

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Title: Lattices and codes with long shadows
Author: Elkies, Noam
Citation: Elkies, Noam D. 1995. Lattices and codes with long shadows. Mathematical Research Letters 2(5): 643-651.
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Abstract: In an earlier paper we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A "characteristic vector" of L is a vector w in L such that 2|(v,w-v) for all v in L; it is known that the characteristic vectors all have norm congruent to n mod 8 and comprise a coset of 2L in L.] Here we use modular forms and the classification of unimodular lattices of rank <24 to find all L whose minimal characteristic vectors have norm n-8. Along the way we also obtain congruences and a lower bound on the kissing number of unimodular lattices with minimal norm 2. We then state and prove analogues of these results for self-dual codes, and relate them directly to the lattice problems via "Construction A".
Other Sources: http://www.mrlonline.org/mrl/1995-002-005/index.html
http://arxiv.org/abs/math/9906086
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2961697

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  • FAS Scholarly Articles [6929]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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