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Application of the cyclotomic Fast Fourier Transform algorithm to the syndrome evaluation problem in classical Reed-Solomon decoders is described. A number of complexity reduction tricks is suggested. Application of the algorithm leads to significant reductions in the complexity of syndrome evaluation. Moreover, automatic generation of the program code… (More)

A novel method for computation of the discrete Fourier transform over a finite field with reduced multiplicative complexity is described. If the number of multiplications is to be minimized, then the novel method for the finite field of even extension degree is the best known method of the discrete Fourier transform computation. A constructive method of… (More)

In this paper we propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speed up of the decoding process of BCH, Reed-Solomon and some other error-correcting codes.

A simple and natural Gao algorithm for decoding algebraic codes is described. Its relation to the Welch-Berlekamp and Euclidean algorithms is given. I. INTRODUCTION In the recent paper, Gao [1] described a simple and natural algorithm for decoding algebraic codes in the class of algorithms decoding up to the designed error-correcting capability. The… (More)

In this paper we suggest a hybrid method for finding toots of error locator polynomials. We first review a fast version of the Chien search algorithm based on the decomposition of the error locator polynomial into a sum of multiples of affine polynomials. We then propose to combine it with modified analytical methods for solution of polynomials of small… (More)

In this paper, following [1, 2, 3, 4, 5, 6, 7] we consider the relations between well-known Fourier transform algorithms.

A simple algorithm for decoding both errors and erasures of Reed-Solomon codes is described.