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. Additionally, we construct non-linear formally self-dual codes and relate them to lattices. (C) 2003 Elsevier B.V. All rights reserved.X11sciescopu