Ideals of the Polynomial Ring for Error Control In Computer Applications

Abstract

This research provides ideals of the polynomial ring associated with the code words of a cyclic code C. If the set of polynomials corresponding to codeword is given by me(c), an ideal of F, it can be shown that C is a cyclic code. Principal ideals of cyclic codes are defined from a new view point involving polynomials. The potentialities of these codes for error control in computer applications are described in detail.  Error coding and decoding use mathematical formulas to encode data at the source into longer words for transmission. Performance of different types of error control codes has been investigated for application in computerized systems. Algebraic geometry over principal ideals of cyclic codes and their applications to error control are also discussed. A code region for optimal codes obtained has been constructed as predicted by Shannon’s Theorem.