Codes over hyperrings

B. Davvaz, T. Musavi

Hyperrings are essentially rings, with approximately modified axioms in which addition or multiplication is a hyperoperation. In this paper, we focus on an important subclass of codes with additional structure called linear codes. Indeed, we introduce the notion of linear codes on finite hyperrings and we present a construction technique of cyclic codes over finite hyperrings. Since polynomial hyperrings are one of the main tools in our study, we analyze them too.