On Cauchy matrices for remainder decoding of Reed-Solomon codes

Authors:
Chingwo Ma
Affiliations:
Venue:
IEEE Communications Letters
Year:
2009

Citing 3
Cited 0

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On the equivalence of two Welch-Berlekamp key equations and their error evaluators

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Fast parallel algorithms for decoding Reed-Solomon codes based on remainder polynomials

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Abstract

It is shown that generalized Cauchy matrices in generator matrices of Reed-Solomon codes can be interpreted by a Lagrange interpolation. The algebraic property of such Cauchy generators is presented. As a main result, a new key equation for the remainder decoding of Reed-Solomon codes is derived. This extends a previous work in Welch's note.