QUANTUM CODES OBTAINED FROM CYCLIC CODES OVER FINITE CHAIN RING

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.