Journal ArticleDOI
A Method for Fast Computation of the Fourier Transform over a Finite Field
TLDR
This work considers the problem of fast computation of the Fourier transform over a finite field by decomposing an arbitrary polynomial into a sum of linearized polynomials.Abstract:
We consider the problem of fast computation of the Fourier transform over a finite field by decomposing an arbitrary polynomial into a sum of linearized polynomials. Examples of algorithms for the Fourier transform with complexity less than that of the best known analogs are given.read more
Citations
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Journal ArticleDOI
Fast algorithms for digital signal processing
TL;DR: This new textbook by R. E. Blahut contains perhaps the most comprehensive coverage of fast algorithms todate, with an emphasis on implementing the two canonical signal processing operations of convolution and discrete Fourier transformation.
Book
Fast Algorithms for Signal Processing
TL;DR: A collection of cyclic convolution algorithms and a collection of Winograd small FFT algorithms for solving Toeplitz systems are presented.
Journal ArticleDOI
Additive Fast Fourier Transforms Over Finite Fields
Shuhong Gao,Todd D. Mateer +1 more
TL;DR: New additive Fast Fourier Transform algorithms based on Taylor expansions over finite fields of characteristic two are presented, which improve previous approaches by Wang and Zhu, Cantor, and von zur Gathen and Gerhard.
Journal ArticleDOI
Cyclotomic FFTs With Reduced Additive Complexities Based on a Novel Common Subexpression Elimination Algorithm
Ning Chen,Zhiyuan Yan +1 more
TL;DR: This paper proposes a novel common subexpression elimination (CSE) algorithm for matrix-vector multiplications over characteristic-2 fields, and uses a weighted sum of the numbers of multiplications and additions as a metric to reduce the additive complexities of cyclotomic fast Fourier transforms (CFFTs).
Journal ArticleDOI
On computing the syndrome polynomial in Reed–Solomon decoder
TL;DR: Application of the cyclotomic fast Fourier transform (FFT) algorithm to the syndrome evaluation problem in classical Reed-Solomon decoders leads to significant reductions in the complexity of syndrome evaluation.
References
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Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Book
Algebraic Coding Theory
TL;DR: This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.
Book
Theory and practice of error control codes
TL;DR: To understand the theoretical framework upon which error-control codes are built and then Algebraic Codes for Data Transmission by Richard E. Blahut, needed, several examples to illustrate the performance of the approximation scheme in practice are needed.
Book
Fast Algorithms for Digital Signal Processing
TL;DR: Fast algorithms for digital signal processing, Fast algorithms fordigital signal processing , and so on.