Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-perfect Lee Codes of Radius 2 and Arbitrarily Large Dimension   A construction of 2-quasi-perfect Lee codes is given over the space $\mathbb
Z_p^n$ for $p$ prime, $p\equiv \pm 5\pmod{12}$ and $n=2[\frac{p}{4}]$. It is
known that there are infinitely many such primes. Golomb and Welch conjectured
that perfect codes for the Lee-metric do not exist for dimension $n\geq 3$ and
radius $r\geq 2$. This conjecture was proved to be true for large radii as well
as for low dimensions. The codes found are very close to be perfect, which
exhibits the hardness of the conjecture. A series of computations show that
related graphs are Ramanujan, which could provide further connections between
Coding and Graph Theories.

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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph