$\mathcal{P}$-schemes and Deterministic Polynomial Factoring over Finite Fields

Zeyu Guo

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arXiv · 1706.10028

$\mathcal{P}$-schemes and Deterministic Polynomial Factoring over Finite Fields

Zeyu Guo

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Abstract

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).

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BibTeX RIS

Zeyu Guo. 2017-09-23. $\mathcal{P}$-schemes and Deterministic Polynomial Factoring over Finite Fields. https://arxiv.org/abs/1706.10028

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