Q-多项式距离正则图的分类及其Delsarte理论是代数组合论中的重要问题。本项目将围绕这两个问题展开研究：1. 研究Q-多项式距离正则图的分类中由著名数学家E.R. Van Dam等人提出的一个子问题：给出有经典参数且b不为1的距离正则图的分类；2. 在Delsarte理论方面，1)利用Terwilliger代数和半定规划理论确定Grassmann图、 H(n,2)的二部半图上码的上界；2)研究折叠n-立方图、奇图上的相对t-设计；3)在有限典型群几何中研究Q-多项式距离正则图上码的上界和相对t-设计。本项目将首次把Terwilliger代数及其表示、强闭包子图和有限典型群几何结合起来研究这个分类问题，同时首次尝试有限典型群几何在Delsarte理论中的应用。这些研究对代数组合论及其相关学科的发展都有重要意义。

The classification and Delsarte theory of Q-polynomial distance-regular graphs are the important problems in the theory of algebraic combinatorics. In this research, we will study these two fundamental problems: 1. We study a subproblem of classification of Q-polynomial distance-regular graphs proposed by famous mathematician E.R. Van Dam et al, that is, classify the distance-regular graphs with classical parameters with b not being 1; 2. For Delsarte theory, 1)we study upper bounds of codes on Grassmann graph and the bipartite half of H(n,2) based on block-diagonalizing the Terwilliger algebra of them and on semidefinite programming; 2)we study relative t-designs on the folded n-cube and odd graph; 3)we also study upper bounds of codes and relative t-designs on these Q-polynomial distance-regular graphs from the geometry of classical groups over finite fields. This project initiates the classification by using together Terwilliger algebra and its representation, strongly regular subgraphs and the geometry of classical groups over finite fields. Also, it is the first time to apply geometry of classical groups over finite fields to Delsarte theory. This proposal can contribute very well for the further developments of algebraic combinatorics and related areas of mathematics.