Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbit Structure of Grassmannian $G_{2, m}$ and a decoder for Grassmann
  code $C(2, m)$   In this manuscript, we consider decoding Grassmann codes, linear codes
associated to Grassmannian of planes in an affine space. We look at the orbit
structure of Grassmannian arising from the natural action of multiplicative
group of certain finite field extension. We project the corresponding Grassmann
code onto these orbits to obtain a few subcodes of certain Reed-Solomon code.
We prove that some of these projected codes contains an information set of the
parent Grassmann code. By improving the efficiency of Peterson's decoding
algorithm for the projected subcodes, we prove that one can correct up to
$\lfloor d-1/2\rfloor$ errors for Grassmann code, where $d$ is the minimum
distance of Grassmann code.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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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: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th