ISSN 2394-5125
 

Research Article 


BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES

P. Moorthy, K. Rajendran.

Abstract
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.

Key words: Commutative ring, prime ideals, filed, nilpotent, encoding and decoding, Frobenius ring and Hamming distance.


 
ARTICLE TOOLS
Abstract
PDF Fulltext
How to cite this articleHow to cite this article
Citation Tools
Related Records
 Articles by P. Moorthy
Articles by K. Rajendran
on Google
on Google Scholar


How to Cite this Article
Pubmed Style

P. Moorthy, K. Rajendran. BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES. JCR. 2020; 7(10): 2161-2166. doi:10.31838/jcr.07.10.372


Web Style

P. Moorthy, K. Rajendran. BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES. http://www.jcreview.com/?mno=123750 [Access: August 17, 2021]. doi:10.31838/jcr.07.10.372


AMA (American Medical Association) Style

P. Moorthy, K. Rajendran. BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES. JCR. 2020; 7(10): 2161-2166. doi:10.31838/jcr.07.10.372



Vancouver/ICMJE Style

P. Moorthy, K. Rajendran. BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES. JCR. (2020), [cited August 17, 2021]; 7(10): 2161-2166. doi:10.31838/jcr.07.10.372



Harvard Style

P. Moorthy, K. Rajendran (2020) BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES. JCR, 7 (10), 2161-2166. doi:10.31838/jcr.07.10.372



Turabian Style

P. Moorthy, K. Rajendran. 2020. BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES. Journal of Critical Reviews, 7 (10), 2161-2166. doi:10.31838/jcr.07.10.372



Chicago Style

P. Moorthy, K. Rajendran. "BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES." Journal of Critical Reviews 7 (2020), 2161-2166. doi:10.31838/jcr.07.10.372



MLA (The Modern Language Association) Style

P. Moorthy, K. Rajendran. "BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES." Journal of Critical Reviews 7.10 (2020), 2161-2166. Print. doi:10.31838/jcr.07.10.372



APA (American Psychological Association) Style

P. Moorthy, K. Rajendran (2020) BOUNDARIES OF COMMUTATIVE RINGS IN CODING TECHNIQUES. Journal of Critical Reviews, 7 (10), 2161-2166. doi:10.31838/jcr.07.10.372