Mathematical Sciences: Computational amd Algorithmic Problems in Design Theory

首席研究员将研究一些计算和算法问题，这些问题与设计理论中的许多研究问题有关。需要研究的最重要的算法问题之一是线性码的同构问题。还将研究有助于他们研究的各种分解问题和算法，重点放在Steiner系统和一般超图的分解上。除了从算法的观点来看有意义之外，所提出的计算研究将为涉及设计、超图、线性码和有限几何的困难问题提供必要的洞察。

The principal investigator will study a number of computational and algorithmic issues which are relevant to many research problems in design theory. One of the most significant algorithmic questions to be studied is the isomorpohism problem for linear codes. Also investigated will be various decomposition problems and algorithms which will aid in their study, with the focus on the decomposition of Steiner systems and hypergraphs in general. Besides being of interest from an algorithmic point of view, the computational studies proposed will provide needed insight into difficult problems involving designs, hypergraphs, linear codes, and finite geometries.