Title :
On cauchy matrices for remainder decoding of reed-solomon codes
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.
Keywords :
Reed-Solomon codes; decoding; interpolation; matrix algebra; Cauchy matrices; Lagrange interpolation; Reed-Solomon codes; algebraic property; generator matrices; remainder decoding; Decoding; Differential algebraic equations; Interpolation; Lagrangian functions; Parity check codes; Polynomials; Reed-Solomon codes; Cauchy matrices, Welch-Berlekamp key equation, Reed-Solomon codes;
Journal_Title :
Communications Letters, IEEE
DOI :
10.1109/LCOMM.2009.091129
