Characterization of codes of ideals of the polynomial ring for control in computer applicatons
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Date
2016-06-01
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Journal ISSN
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Publisher
C o u n c i l f o r I n n o v a t i v e R e s e a r c h : J o u r n a l o f A d v a n c e s i n M a t h e m a t i c s
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 Noetherian rings are closed in polynomial addition and multiplication.This property has been used to characterize the polynomial ring F_2^n[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.
Description
Keywords
Polynomial ring, Error detection, Error correction, Code region.