CHARACTERIZATION OF CODES OF IDEALS OF THE POLYNOMIAL RING F30 2 [x] Mod X30 1 FOR ERROR CONTROL IN COMPUTER APPLICATONS
Published 2016 · Mathematics
The study of ideals in algebraic number system has contributed immensely inpreserving the notion of unique factorization in rings of algebraic integers and inproving Fermat's last Theorem. Recent research has revealed that ideals in Noethe-rian rings are closed in polynomial addition and multiplication.This property hasbeen 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.