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Structure prediction for error pattern and extension of Welch-Berlekamp theorem

忻鼎稼

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Abstract

As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH bound

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As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH bound

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Available abstract

As the Welch-Berlekamp (W-B) theorem accurately predicts structure of error locator polynomials of the error patterns, it results in the Welch-Berlekamp algorithm of decoding cyclic codes. However, it is only valid within the BCH bound. Now, a prediction formula for error locator determination is presented based on the study of theory of minimal homogeneous interpolation problem, which extends the Welch-Berlekamp theorem and expands the Welch-Berlekamp algorithm so that the constraint from the BCH bound

Key concepts: BCH code, Mathematics, Constraint (computer-aided design), Extension (predicate logic), Decoding methods, Discrete mathematics, Algorithm, Error detection and correction

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