Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1607-49
Keywords
Discrete Fourier transform, partial Hasse derivative, Reed‒Solomon codes
First Page
349
Last Page
359
Recommended Citation
MAZROOEI, M, RAHIMI, L, & SAHAMI, N (2018). Two-dimensional generalized discrete Fourier transform and related quasi-cyclic Reed‒Solomon codes. Turkish Journal of Mathematics 42 (1): 349-359. https://doi.org/10.3906/mat-1607-49
