Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Codes over rings of size $p^2$ and lattices over imaginary quadratic
  fields   Let $\ell>0$ be a square-free integer congruent to 3 mod 4 and $\O_K$ the
ring of integers of the imaginary quadratic field $K=Q(\sqrt{-\ell})$. Codes
$C$ over rings $\O_K / p \O_K$ determine lattices $\Lambda_\ell (C) $ over $K$.
If $ p \nmid \ell$ then the ring $\R:=\O_K / p \O_K$ is isomorphic to
$\F_{p^2}$ or $\F_p \times \F_p$. Given a code $C$ over $\R$, theta functions
on the corresponding lattices are defined. These theta series
$\theta_{\Lambda_{\ell}(C)}$ can be written in terms of the complete weight
enumerator of $C$. We show that for any two $\ell < \ell^\prime$ the first
$\frac {\ell + 1} 4$ terms of their corresponding theta functions are the same.
Moreover, we conjecture that for $\ell > \frac {p(n+1)(n+2)} 2$ there is a
unique complete weight enumerator corresponding to a given theta function. We
verify the conjecture for primes $p< 7$ and $\ell \leq 59$.

16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an