Najme Sahami - Department of mathematical sciences, University of Kashan, Kashan, Isfahan, Iran.
Majid Mazrooei - Department of mathematical sciences, University of Kashan, Kashan, Isfahan, Iran.

In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.

Generalized Discrete Fourier Transform, Hasse Derivatives, Linear Codes, Reed-Solomon Codes