Two-dimensional generalized discrete Fourier transform and related quasi-cyclic Reed‒Solomon codes

Authors : Majid Mazrooei, Lale Rahimi, Najme Sahami

Pages : 349-359

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :Using the concept of the partial Hasse derivative, we introduce a generalization of the classical 2-dimensional discrete Fourier transform, which will be called 2D-GDFT. Begining with the basic properties of 2D-GDFT, we proceed to study its computational aspects as well as the inverse transform, which necessitate the development of a faster way to calculate the 2D-GDFT. As an application, we will employ 2D-GDFT to construct a new family of quasi-cyclic linear codes that can be assumed to be a generalization of Reed‒Solomon codes.
Keywords : Discrete Fourier transform, partial Hasse derivative, Reed‒Solomon codes