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Splitting the shadow

Splitting the shadow.
descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 2003 English Publisher:Elsevier BVJournal:Discrete Mathematics, volume 270, pages 43-60 (issn: 0012-365X, Copyright policy )
Authors: Bonnecaze, A; Choie, Y; Dougherty, ST; Sole, P;

doi: 10.1016/s0012-365x(02)00865-8

Splitting the shadow

Abstract

Let \(L\) be an odd unimodular lattice of rank \(n\). Let \(L_0\) denote the sublattice of even norm vectors with \(L_2\) the unique non-trivial coset in \(L\), and let \(L_1\) and \(L_3\) be the other two cosets in \(L^*_0\) with the shadow \(S=L_1 \cup L_3\). The theta series of \(L_1\) and \(L_3\) are evaluated through the Jacobi theta series attached to \(L\) and to a certain vector. An analogous theorem for codes over \({\mathbb Z}_{2k}\) is derived. Some applications are considered when theta series can be calculated explicitly.

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Keywords

unimodular lattices, Geometry of numbers, Relations with coding theory, Theoretical Computer Science, II CODES, self-dual codes, shadows, Unimodular lattices, Jacobi forms, Self-dual codes, Discrete Mathematics and Combinatorics, [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], LATTICES, Shadows, Linear codes (general theory)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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