Mathematical Sciences: Computational amd Algorithmic Problems in Design Theory

首席研究员将研究一些与设计理论中的许多研究问题相关的计算和算法问题。线性码的同构问题是目前最重要的算法问题之一。还将研究各种分解问题和算法，这将有助于他们的研究，重点是一般的斯坦纳系统和超图的分解。除了从算法的角度来看，所提出的计算研究将为涉及设计、超图、线性编码和有限几何的难题提供必要的见解。

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.