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

Majid Mazrooei | Zendy; Lale Rahimi | Zendy; Najme Sahami | Zendy

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

Author(s) -

Majid Mazrooei,

Lale Rahimi,

Najme Sahami

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1607-49

Subject(s) - mathematics , generalization , discrete fourier transform (general) , fourier transform , inverse , construct (python library) , fourier transform on finite groups , short time fourier transform , fractional fourier transform , mathematical analysis , fourier analysis , computer science , geometry , programming language

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.

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