Two-dimensional generalized discrete Fourier transform and related quasi-cyclicReed{Solomon codes

Abstract

Using the concept of the partial Hasse derivative, we introduce a generalization of the classical 2-dimensionaldiscrete Fourier transform, which will be called 2D-GDFT. Begining with the basic properties of 2D-GDFT, we proceedto study its computational aspects as well as the inverse transform, which necessitate the development of a faster wayto calculate the 2D-GDFT. As an application, we will employ 2D-GDFT to construct a new family of quasi-cyclic linearcodes that can be assumed to be a generalization of Reed{Solomon codes.