Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantizing Using Lattice Intersections   The usual quantizer based on an n-dimensional lattice L maps a point x in R^n
to a closest lattice point. Suppose L is the intersection of lattices L_1, ...,
L_r. Then one may instead combine the information obtained by simultaneously
quantizing x with respect to each of the L_i. This corresponds to decomposing
R^n into a honeycomb of cells which are the intersections of the Voronoi cells
for the L_i, and identifying the cell to which x belongs. This paper shows how
to write several standard lattices (the face-centered and body-centered cubic
lattices, the root lattices D_4, E_6*, E_8, the Coxeter-Todd, Barnes-Wall and
Leech lattices, etc.) in a canonical way as intersections of a small number of
simpler, decomposable, lattices. The cells of the honeycombs are given
explicitly and the mean squared quantizing error calculated in the cases when
the intersection lattice is the face-centered or body-centered cubic lattice or
the lattice D_4.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph