Abstract

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.

Keywords: hyperring; hyperring of polynomials; hyperideal; linear code; cyclic code

MSC: 20N20, 16Y99, 94B05

Pages:  26$-$38     

Volume  68 ,  Issue  1 ,  2016