Title :
New generalizations of the Reed-Muller codes--I: Primitive codes
Author :
Kasami, Tadao ; Lin, Shu ; Peterson, Wesley W.
fDate :
3/1/1968 12:00:00 AM
Abstract :
First it is shown that all binary Reed-Muller codes with one digit dropped can be made cyclic by rearranging the digits. Then a natural generalization to the nonbinary case is presented, which also includes the Reed-Muller codes and Reed-Solomon codes as special cases. The generator polynomial is characterized and the minimum weight is established. Finally, some results on weight distribution are given.
Keywords :
Cyclic codes; Reed-Muller codes; Aerospace engineering; Character generation; Control engineering; Information theory; Laboratories; Polynomials; Reed-Solomon codes; Shift registers; TV; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.1968.1054127
