Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counterexample to the $l$-modular Belfiore-Sol\'e Conjecture   We show that the secrecy function conjecture that states that the maximum of
the secrecy function of an $l$-modular lattice occurs at $1/\sqrt{l}$ is false,
by proving that the 4-modular lattice $C^(4) = \mathbb{Z} \oplus
\sqrt{2}\mathbb{Z} \oplus 2\mathbb{Z}$ fails to satisfy this conjecture. We
also indicate how the secrecy function must be modified in the $l$-modular case
to have a more reasonable chance for it to have a maximum at $1/\sqrt{l}$, and
show that the conjecture, modified with this new secrecy function, is true for
various odd 2-modular lattices.

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The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
13
The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess