Journal ArticleDOI
A method for computation of the discrete Fourier transform over a finite field
TLDR
The proposed computation method for the discrete Fourier transform is based on factorizing the transform matrix into a product of a binary block circulant matrix and a diagonal block circULant matrix.Abstract:
The discrete Fourier transform over a finite field finds applications in algebraic coding theory. The proposed computation method for the discrete Fourier transform is based on factorizing the transform matrix into a product of a binary block circulant matrix and a diagonal block circulant matrix.read more
Citations
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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).
Posted Content
Complexity Analysis of Reed-Solomon Decoding over GF(2^m) Without Using Syndromes
Ning Chen,Zhiyuan Yan +1 more
TL;DR: The complexity of syndromeless decoding, and compare it to that of syndrome-based decoding, is investigated, and aiming to provide guidelines to practical applications, focuses on RS codes over characteristic-2 fields, for which some multiplicative FFT techniques are not applicable.
Journal ArticleDOI
Composite Cyclotomic Fourier Transforms With Reduced Complexities
TL;DR: This paper proposes composite cyclotomic Fourier transforms (CCFTs), which achieve lower overall complexities for moderate to long lengths and the improvement significantly increases as the length grows.
References
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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.
Journal ArticleDOI
Discrete Fourier transforms when the number of data samples is prime
TL;DR: The discrete Fourier transform of a sequence of N points, where N is a prime number, is shown to be essentially a circular correlation, which permits the discrete Fouriers transform to be computed by means of a fast Fouriertransform algorithm, with the associated increase in speed, even though N is prime.
Journal ArticleDOI
A Method for Fast Computation of the Fourier Transform over a Finite Field
TL;DR: 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.
Journal ArticleDOI
A fast algorithm for the Fourier transform over finite fields and its VLSI implementation
TL;DR: An algorithm for computing the Fourier transform over any finite field GF(p/sup m/) that requires only O(n(log n)/sup 2//4) additions and the same number of multiplications for an n-point transform and allows in some fields a further reduction of the number of multiplier additions.