Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The MacWilliams identity for $m$-spotty weight enumerator over
  $\mathbb{F}_2+u\mathbb{F}_2+\cdots+u^{m-1}\mathbb{F}_2$   Past few years have seen an extensive use of RAM chips with wide I/O data
(e.g. 16, 32, 64 bits) in computer memory systems. These chips are highly
vulnerable to a special type of byte error, called an $m$-spotty byte error,
which can be effectively detected or corrected using byte error-control codes.
The MacWilliams identity provides the relationship between the weight
distribution of a code and that of its dual. The main purpose of this paper is
to present a version of the MacWilliams identity for $m$-spotty weight
enumerators over
$\mathbbm{F}_{2}+u\mathbbm{F}_{2}+\cdots+u^{m-1}\mathbbm{F}_{2}$ (shortly
$R_{u, m, 2}$).

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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: math-ph