  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 by 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$. Another famous theorem of
Graham Higman, the founder-editor of Journal of Algebra, which is true for an
integral domain or a field can be extended to a halidon ring. 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
