Title :
Polynomial codes and principal ideal rings
Author :
Cazaran, Jilyana ; Kelarev, Andrei V.
Author_Institution :
Dept. of Math., Tasmania Univ., Hobart, Tas., Australia
fDate :
29 Jun-4 Jul 1997
Abstract :
Conditions are given which determine when the ring R=S[x1 , ..., xn]/(f1(x1), ..., fn (xn)) is a principal ideal ring where either S=Z m and R is finite or S is a field. If S and R are both finite then an ideal C of R is a linear code. Hence one obtains necessary and sufficient conditions for the existence of a single generator polynomial of C. If S is a finite field and fi(x i)=xili-1 for certain integers li for i=1 to n then the ideals of R are multivariate cyclic codes and include the class of generalized Reed-Muller codes
Keywords :
Reed-Muller codes; cyclic codes; linear codes; polynomials; finite field; generalized Reed-Muller codes; linear code; multivariate cyclic codes; polynomial codes; principal ideal rings; single generator polynomial; Australia; Galois fields; Hamming distance; Linear code; Mathematics; Polynomials; Sufficient conditions;
Conference_Titel :
Information Theory. 1997. Proceedings., 1997 IEEE International Symposium on
Conference_Location :
Ulm
Print_ISBN :
0-7803-3956-8
DOI :
10.1109/ISIT.1997.613439
