On Cyclic Codes of a Given Length N

The theory of Error–correcting codes is eminently indispensable in our life. In this direction, one of the most important developments was the theory of cyclic codes, which is traditionally embedded in the language of ring theory. In this paper our interest to motivate the ring theoretic formulation of coding theory and draw attention to the paths used to determine the cyclic codes generated by the idempotent generators in the ring ? ? 1 N N q R ? F X X ? of a given length N over the finite field q F with explicit settings. References S. K. Arora and M. Pruthi, Minimal cyclic codes of length , Finite Field and 2 n p Appl. , 5(1999), 177-187. J. H. van Lint. Introduction to Coding Theory, Springer-Verlag, BerlinHeidelberg, 3rd revised and expended ed. edition, 1982-1999.