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dc.contributor.authorElkies, Noam
dc.date.accessioned2009-05-20T15:05:18Z
dc.date.issued1995
dc.identifier.citationElkies, Noam D. 1995. Lattices and codes with long shadows. Mathematical Research Letters 2(5): 643-651.en
dc.identifier.issn1073-2780en
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:2961697
dc.description.abstractIn 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".en
dc.description.sponsorshipMathematicsen
dc.language.isoen_USen
dc.publisherInternational Pressen
dc.relation.hasversionhttp://www.mrlonline.org/mrl/1995-002-005/index.htmlen
dc.relation.hasversionhttp://arxiv.org/abs/math/9906086en
dash.licenseLAA
dc.subjectnumber theoryen
dc.titleLattices and codes with long shadowsen
dc.relation.journalMathematical Research Lettersen
dash.depositing.authorElkies, Noam
dash.contributor.affiliatedElkies, Noam


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