The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization cyclic In this paper, we study over finite Krasner hyperfields which characterize them by their generating polynomial. Moreover, dual these finding parity check

Multirings are objects like rings but with multi-valued addition. They are a variant of other objects called hyperrings, defined by Krasner [12], [13]. In [16] the second author defines multirings, introduces a certain special class of multirings called real reduced multirings, defines a natural reflection A Ã Qred(A) from the category of multirings satisfying −1 / ∈ ∑ A2 to the full subcategor...

We develop a theory of multiplicities roots for polynomials over hyperfields and use this to provide unified conceptual proof both Descartes' rule signs Newton's "polygon rule".

This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the "sum" of two elements is a subset of the structure. The results in this paper show that these structures .cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that the structural results for hyperfields and...

In this article, first we generalize the concept of complete parts in hyperrings by introducing the concept R-parts in hyperrings and then we study R-closures in hyperrings. Finally we characterize R-closures in hyperfields.

We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the e↵ect of the screening parameter is a change of measure of the underlying metric space; also indicating a conditioned random walker biased by the choice of measure. A continuum of shape fields is created, by varying the screening parameter or equivalently the bias of the random walk...