Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Gabidulin Codes cannot be List Decoded Efficiently at any Radius   Gabidulin codes can be seen as the rank-metric equivalent of Reed-Solomon
codes. It was recently proven, using subspace polynomials, that Gabidulin codes
cannot be list decoded beyond the so-called Johnson radius. In another result,
cyclic subspace codes were constructed by inspecting the connection between
subspaces and their subspace polynomials. In this paper, these subspace codes
are used to prove two bounds on the list size in decoding certain Gabidulin
codes. The first bound is an existential one, showing that exponentially-sized
lists exist for codes with specific parameters. The second bound presents
exponentially-sized lists explicitly, for a different set of parameters. Both
bounds rule out the possibility of efficiently list decoding several families
of Gabidulin codes for any radius beyond half the minimum distance. Such a
result was known so far only for non-linear rank-metric codes, and not for
Gabidulin codes. Using a standard operation called lifting, identical results
also follow for an important class of constant dimension subspace codes.

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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: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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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: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom