In an earlier paper (math. NT/9906019) we showed that any integral unimodular lattice L of
rank n which is not isometric with Z^ n has a characteristic vector of norm at most n-8.[A" …

In an earlier paper we showed that any integral unimodular lattice L of rank n which is not
isometric with Z^ n has a characteristic vector of norm at most n-8.[A" characteristic vector" of …

We study self-dual codes over certain finite rings which are quotients of quadratic imaginary
fields or of totally definite quaternion fields over Q. A natural weight taking two different …

Let W (z)= 1+ Ad ezmidr+ AdCl ewrim+ lM+... be a modular form of weight n for the full
modular group. Then for every constant b there exists an n,= n,,(b) such that if d> n/6-b and …

Recently shadows of unimodular lattices have been defined to derive upper bounds on the
minimum norm of Type~ I lattices. In this paper we study shadows of lattices mostly to …

All the lattices under discussion here are understood to be unimodular $\doubz $-lattices in
$\IR\sp {n} $. A characteristic vector of a lattice L is a vector $ w\in L $ such that $ w\cdot …

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 …

Let η be a natural number with η= 0 (mod 8) and C a selfdual ternary [n, n/2] code with
minimal weight d. The main result of this work is that we can construct a positive definite …

The theory of integral quadratic forms has a long history. Here we restrict ourselves to the
theory of definite even unimodular quadratic forms. If the quadratic form is definite, the theory …

With the help of some new results about weight enumerators of self-dual codes over Z _4 we
investigate a class of double circulant codes over Z _4, one of which leads to an extremal …