Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Key Equation for One-Point Codes   For Reed-Solomon codes, the key equation relates the syndrome
polynomial---computed from the parity check matrix and the received vector---to
two unknown polynomials, the locator and the evaluator. The roots of the
locator polynomial identify the error positions. The evaluator polynomial,
along with the derivative of the locator polynomial, gives the error values via
the Forney formula. The Berlekamp-Massey algorithm efficiently computes the two
unknown polynomials.
  This chapter shows how the key equation, the Berlekamp-Massey algorithm, the
Forney formula, and another formula for error evaluation due to Horiguchi all
generalize in a natural way to one-point codes. The algorithm presented here is
based on K\"otter's adaptation of Sakata's algorithm.

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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin