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.
MAZROOEI, MAJID; RAHIMI, LALE; and SAHAMI, NAJME
"Two-dimensional generalized discrete Fourier transform and related quasi-cyclic Reed‒Solomon codes,"
Turkish Journal of Mathematics: Vol. 42:
1, Article 29.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss1/29