We define the complete joint weight enumerator in genus g for codes over Z(2k) and use it to study self-dual codes and their shadows. These weight enumerators are related to the theta series of the associated lattices and Siegel and Jacobi forms are formed from these series. / X / 1 / 1 / 3 / scie / scopus
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 se...
We introduce the finite ring S-2m = Z(2m) + iZ(2m). We develop a theory of self-dual codes over this ring and relate self-dual codes over this ring to complex unimodular lattices. We describe a theory of shadows for these codes and lattices. We construct a gray map from this ring to the ring Z(2m) and relate codes over these rings, giving special a...
