CHARACTERIZATION OF CODES OF IDEALS OF THE POLYNOMIAL RING F30 2 [x] mod ô€€€ x30 ô€€€ 1  FOR ERROR CONTROL IN COMPUTER APPLICATONS

Maurice Oduor; Olege Fanuel; Aywa Shem; Okaka A Colleta

doi:10.24297/jam.v12i5.260

CHARACTERIZATION OF CODES OF IDEALS OF THE POLYNOMIAL RING F30 2 [x] mod ô€€€ x30 ô€€€ 1 FOR ERROR CONTROL IN COMPUTER APPLICATONS

Authors

Maurice Oduor Maseno University, Maseno
Olege Fanuel Department of Mathematics Masinde Muliro University of Science and Technology P.O. Box 190-50100, Kakamega
Aywa Shem Kibabii University P.O. Box 1699-50200, Bungoma
Okaka A Colleta Department of Mathematics Masinde Muliro University of Science and Technology P.O. Box 190-50100, Kakamega

DOI:

https://doi.org/10.24297/jam.v12i5.260

Keywords:

Polynomial ring, Error detection, Error correction, Code region.

Abstract

The study of ideals in algebraic number system has contributed immensely in preserving the notion of unique factorization in rings of algebraic integers and in proving Fermat's last Theorem. Recent research has revealed that ideals in Noethe-rian rings are closed in polynomial addition and multiplication.This property has been used to characterize the polynomial ring Fn 2 [x] mod (xn 1) for error control. In this research we generate ideals of the polynomial ring using GAP software and characterize the polycodewords using Shannon's Code region and Manin's bound.

Downloads

Download data is not yet available.

Author Biography

Aywa Shem, Kibabii University P.O. Box 1699-50200, Bungoma

Department of Mathematics

Downloads

Published

2016-06-30

How to Cite

Oduor, M., Fanuel, O., Shem, A., & Colleta, O. A. (2016). CHARACTERIZATION OF CODES OF IDEALS OF THE POLYNOMIAL RING F30 2 [x] mod ô€€€ x30 ô€€€ 1 FOR ERROR CONTROL IN COMPUTER APPLICATONS. JOURNAL OF ADVANCES IN MATHEMATICS, 12(5), 6238–6247. https://doi.org/10.24297/jam.v12i5.260