About Euclidean Codes in Rings
K. Abdelmoumen *
Faculty of Science and Technology Fez, Morocco
H. Ben-azza
Moulay IsmaÏl University, Ensam-Meknès, Morocco
M. Najmeddine
Moulay IsmaÏl University, Ensam-Meknès, Morocco
*Author to whom correspondence should be addressed.
Abstract
In this paper, we construct codes over rings which have a Euclidean division, in the commutative and non commutative cases. Such construction generalizes Reed-Solomon codes. We exemplify the construction for Gaussian integers and Lipschitz quaternions.
Keywords: Coding theory, Euclidean rings, Gaussian integers, quaternions