Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Folded Algebraic Geometric Codes From Galois Extensions   We describe a new class of list decodable codes based on Galois extensions of
function fields and present a list decoding algorithm. These codes are obtained
as a result of folding the set of rational places of a function field using
certain elements (automorphisms) from the Galois group of the extension. This
work is an extension of Folded Reed Solomon codes to the setting of Algebraic
Geometric codes. We describe two constructions based on this framework
depending on if the order of the automorphism used to fold the code is large or
small compared to the block length. When the automorphism is of large order,
the codes have polynomially bounded list size in the worst case. This
construction gives codes of rate $R$ over an alphabet of size independent of
block length that can correct a fraction of $1-R-\epsilon$ errors subject to
the existence of asymptotically good towers of function fields with large
automorphisms. The second construction addresses the case when the order of the
element used to fold is small compared to the block length. In this case a
heuristic analysis shows that for a random received word, the expected list
size and the running time of the decoding algorithm are bounded by a polynomial
in the block length. When applied to the Garcia-Stichtenoth tower, this yields
codes of rate $R$ over an alphabet of size
$(\frac{1}{\epsilon^2})^{O(\frac{1}{\epsilon})}$, that can correct a fraction
of $1-R-\epsilon$ errors.

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The categories of this paper are: gr-qc
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The categories of this paper are: physics
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: adap-org