Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Octonary Codes and their Covering Radii   This paper introduces new reduction and torsion codes for an octonary code
and determines their basic properties. These could be useful for the
classification of self-orthogonal and self dual codes over $\mathbb{Z}_8$. We
also focus our attention on covering radius problem of octonary codes. In
particular, we determine lower and upper bounds of the covering radius of
several classes of Repetition codes, Simplex codes of Type $\alpha$ and Type
$\beta$ and their duals, MacDonald codes, and Reed-Muller codes over
$\mathbb{Z}_8$.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: ao-sci