Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dynamical System-based Key Equation for Decoding One-Point
  Algebraic-Geometry Codes   A closer look at linear recurring sequences allowed us to define the
multiplication of a univariate polynomial and a sequence, viewed as a power
series with another variable, resulting in another sequence. Extending this
operation, one gets the multiplication of matrices of multivariate polynomials
and vectors of powers series. A dynamical system, according to U. Oberst is
then the kernel of the linear mapping of modules defined by a polynomial matrix
by this operation. Applying these tools in the decoding of the so-called one
point algebraic-geometry codes, after showing that the syndrome array, which is
the general transform of the error in a received word is a linear recurring
sequence, we construct a dynamical system. We then prove that this array is the
solution of Cauchy's homogeneous equations with respect to the dynamical
system. The aim of the Berlekamp-Massey-Sakata Algorithm in the decoding
process being the determination of the syndrome array, we have proved that in
fact, this algorithm solves the Cauchy's homogeneous equations with respect to
a dynamical system.

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The categories of this paper are: physics
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
16
The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci