Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic geometry codes with complementary duals exceed the asymptotic
  Gilbert-Varshamov bound   It was shown by Massey that linear complementary dual (LCD for short) codes
are asymptotically good. In 2004, Sendrier proved that LCD codes meet the
asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound
still remains to be the best asymptotical lower bound for LCD codes. In this
paper, we show that an algebraic geometry code over a finite field of even
characteristic is equivalent to an LCD code and consequently there exists a
family of LCD codes that are equivalent to algebraic geometry codes and exceed
the asymptotical GV bound.

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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat