  Halidon rings are rings with a unit element, containing a primitive $m^{th}$
root of unity and $m$ is invertible in the ring. The field of complex numbers
is a halidon ring with any index $ m \geq 1$. In this article, the author
examines the computational aspects of a new class of rings called Halidon rings
and their applications with the help of computer codes. In representation
theory, Maschke's theorem has an important role in studying the irreducible
subrepresentations of a given group representation. Mainly the study is related
to a finite field of characteristic which does not divide the order of the
given finite group or the field of real or complex numbers. This article also
examines the possibility of replacing the finite field in the theorem with
halidon rings in such a way that the theorem is still valid. Halidon rings are
rings with the unit element, containing a primitive $m^{th}$ root of unity and
$m$ is invertible in the ring. The field of complex numbers is a halidon ring
with any index $ m \geq 1$. Some computer codes have been developed to
establish the existence of halidon rings which are not fields and the
computation of units, involutions and idempotents in both halidon rings and
halidon group rings. The application halidon rings in Discrete Fourier
Transform (DFT) is studied and two computer codes have been developed to
calculate DFT and inverse DFT
