Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Codes Associated with Orthogonal Groups and Power Moments of Kloosterman
  Sums   In this paper, we construct three binary linear codes $C(SO^{-}(2,q))$,
$C(O^{-}(2,q))$, $C(SO^{-}(4,q))$, respectively associated with the orthogonal
groups $SO^{-}(2,q)$, $O^{-}(2,q)$, $SO^{-}(4,q)$, with $q$ powers of two. Then
we obtain recursive formulas for the power moments of Kloosterman and
2-dimensional Kloosterman sums in terms of the frequencies of weights in the
codes. This is done via Pless power moment identity and by utilizing the
explicit expressions of Gauss sums for the orthogonal groups. We emphasize
that, when the recursive formulas for the power moments of Kloosterman sums are
compared, the present one is computationally more effective than the previous
one constructed from the special linear group $SL(2,q)$. We illustrate our
results with some examples.

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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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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: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: physics