Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binary Linear Codes From Vectorial Boolean Functions and Their Weight
  Distribution   Binary linear codes with good parameters have important applications in
secret sharing schemes, authentication codes, association schemes, and consumer
electronics and communications. In this paper, we construct several classes of
binary linear codes from vectorial Boolean functions and determine their
parameters, by further studying a generic construction developed by Ding
\emph{et al.} recently. First, by employing perfect nonlinear functions and
almost bent functions, we obtain several classes of six-weight linear codes
which contains the all-one codeword. Second, we investigate a subcode of any
linear code mentioned above and consider its parameters. When the vectorial
Boolean function is a perfect nonlinear function or a Gold function in odd
dimension, we can completely determine the weight distribution of this subcode.
Besides, our linear codes have larger dimensions than the ones by Ding et al.'s
generic construction.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph