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Splitting the shadow |
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| Authors: | A. Bonnecaze, Y. Choie, S.T. Dougherty,P. Sol |
| Affiliation: | aIAAI et Laboratoire LIF, Centre de Mathématiques et Informatique, 39 rue Joliot-Curie, F-13453 Marseille Cedex 13, France bDepartment of Mathematics, POSTECH, Pohang, South Korea cDepartment of Mathematics, University of Scranton, Scranton, PA 18510, USA dCNRS-I3S, ESSI, Route des Colles, 06 903 Sophia Antipolis, France |
| Abstract: | We derive formulae for the theta series of the two translates of the even sublattice L0 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. |
| Keywords: | Jacobi forms Unimodular lattices Self-dual codes Shadows |
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