Ramazan Duran

Afyon Kocatepe University | AKU · Department of Mathematics

A quaternion, each component is in integers, is called a Lipschitz integer. A Lipschitz integer is called a primitive Lipschitz integer just if the greatest common divisor of its components is one. Complex-valued codes over Lipschitz integers are obtained accompanied by a respective modulo function. In this study, we demonstrate that some primitive...

Considering error-correcting codes over Hurwitz integers, prime Hurwitz integers are considered. On the other hand, considering transmission over Gaussian channel, Hurwitz integers, whose the norm is either a prime integer or not a prime integer, are considered. In this study, we consider Hurwitz integers, the greatest common divisor of components...

Let α be a prime Hurwitz integer. Hα, which is the set of residual class with respect to related modulo function in the rings of Hurwitz integers, is a subset of H, which is the set of all Hurwitz integers. We consider left congruent modulo α and, the domain of related modulo function in this study is ZN(α), which is residual class ring of ordinary...