$\mathcal{P}$-schemes and Deterministic Polynomial Factoring over Finite Fields
نویسنده
چکیده
We introduce a family of mathematical objects called $\mathcal{P}$-schemes, where $\mathcal{P}$ is a poset of subgroups of a finite group $G$. A $\mathcal{P}$-scheme is a collection of partitions of the right coset spaces $H\backslash G$, indexed by $H\in\mathcal{P}$, that satisfies a list of axioms. These objects generalize the classical notion of association schemes as well as the notion of $m$-schemes (Ivanyos et al. 2009). Based on $\mathcal{P}$-schemes, we develop a unifying framework for the problem of deterministic factoring of univariate polynomials over finite fields under the generalized Riemann hypothesis (GRH).
منابع مشابه
P-schemes: a unifying framework for deterministic polynomial factoring over finite fields
We introduce a family of mathematical objects called P-schemes, generalizing the notions of association schemes andm-schemes [IKS09]. Based on these objects, we develop a unifying framework for deterministic polynomial factoring over finite fields under the generalized Riemann hypothesis (GRH). It allows us to not only recover most of the known results but also discover new ones. In particular,...
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