Codes over hyperrings
Keywords:
hyperring, hyperring of polynomials, hyperideal, linear code, cyclic codeSubjects:
20N20, 16Y99, 94B05Abstract
Hyperrings are essentially rings, withapproximately 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 linearcodes. Indeed, we introduce the notion of linear codes on finite hyperrings and we present a constructiontechnique of cyclic codes over finite hyperrings. Since polynomial hyperrings are one of the maintools in our study, we analyze them too.
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2016-01-15
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This work is licensed under a Creative Commons Attribution 4.0 International License.