BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES

This paper is concerned towards the coding techniques over the commutative rings. Further the
fundamental and foundation concepts of coding theory and its organization of structure establishment through
commutative rings are discussed. The study of huge relation between encoding and decoding theory and how it is
well connected through commutative rings are revealed through diverse theorems. Ideals and nilpotent along with
commutative rings are together used to bring out the perfect codes. These exhibited perfect code’s are generated
according to Hamming distance theory and commutative rings. To enrich our results, the commutative ring is
embedded along with Frobenius ring to accomplish the perfect code through Euclidean and orthogonal inner
product.