Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattices and codes with long shadows   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 "characteristic vector" of L is a vector w in L such
that 2|(v,w-v) for all v in L; it is known that the characteristic vectors all
have norm congruent to n mod 8 and comprise a coset of 2L in L.] Here we use
modular forms and the classification of unimodular lattices of rank <24 to find
all L whose minimal characteristic vectors have norm n-8. Along the way we also
obtain congruences and a lower bound on the kissing number of unimodular
lattices with minimal norm 2. We then state and prove analogues of these
results for self-dual codes, and relate them directly to the lattice problems
via "Construction A".

30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga