Abstract:
The main objective of this project work is to discuss about quantum codes obtained from
cyclic codes over finite chain ring. In coding theory, there are different methods to construct
quantum codes from other code within the given code lengths, from that cyclic codes over
finite ring is one method. Some relevant journals and books were to construct quantum codes
from cyclic codes. In this Project important preliminary concept, examples, lemmas and
theorems were presented to make the concept for the construction of quantum codes from
cyclic codes over finite ring. In order to study the construction of quantum codes by using
cyclic codes depending on the lengths of code and using different examples by extending the
lengths of codes with even and odd lengths. To construct quantum codes from cyclic codes
with lengths n is important to determine the parameters of the codes to get good quantum
codes from cyclic codes. Other properties on the quantum codes from cyclic codes over rings
such as self-dual, self-orthogonal and ideal structures were discussed. We showed that the
lengths of codes increases with its parameter due to this we can derive good quantum codes
from cyclic codes to correct and detect errors easily from quantum information systems.
