Splitting the shadow

We derive formulae for the theta series of the two translates of the even sublattice L 0 of an odd unimodular lattice L that constitute the shadow of L. The proof rests on special evaluations of the Jacobi theta series attached to L and to a certain vector. We produce an analogous theorem for codes....

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Bibliographic Details
Published in:Discrete mathematics 2003-08, Vol.270 (1), p.43-60
Main Authors: Bonnecaze, A., Choie, Y., Dougherty, S.T., Solé, P.
Format: Article
Language:English
Subjects:
Algebra
Algebraic combinatorics
Combinatorics
Combinatorics. Ordered structures
Computer Science
Exact sciences and technology
Information Theory
Jacobi forms
Mathematics
Number theory
Order, lattices, ordered algebraic structures
Sciences and techniques of general use
Self-dual codes
Shadows
Unimodular lattices
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Summary:We derive formulae for the theta series of the two translates of the even sublattice L 0 of an odd unimodular lattice L that constitute the shadow of L. The proof rests on special evaluations of the Jacobi theta series attached to L and to a certain vector. We produce an analogous theorem for codes. Additionally, we construct non-linear formally self-dual codes and relate them to lattices.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(02)00865-8