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

Authors

MAJID MAZROOEI
LALE RAHIMI
NAJME SAHAMI

DOI

10.3906/mat-1607-49

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

First Page

349

Last Page

359

Recommended Citation

MAZROOEI, MAJID; RAHIMI, LALE; and SAHAMI, NAJME (2018) "Two-dimensional generalized discrete Fourier transform and related quasi-cyclic Reed‒Solomon codes," Turkish Journal of Mathematics: Vol. 42: No. 1, Article 29. https://doi.org/10.3906/mat-1607-49
Available at: https://journals.tubitak.gov.tr/math/vol42/iss1/29