Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of $\Delta$-divisible linear codes spanned by codewords
  of weight $\Delta$   We classify all $q$-ary $\Delta$-divisible linear codes which are spanned by
codewords of weight $\Delta$. The basic building blocks are the simplex codes,
and for $q=2$ additionally the first order Reed-Muller codes and the parity
check codes. This generalizes a result of Pless and Sloane, where the binary
self-orthogonal codes spanned by codewords of weight $4$ have been classified,
which is the case $q=2$ and $\Delta=4$ of our classification. As an
application, we give an alternative proof of a theorem of Liu on binary
$\Delta$-divisible codes of length $4\Delta$ in the projective case.

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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: cs