有限域上的射影几何是有限几何中的一大类,其结构已被广泛研究.本文利用射影空间中的面构造了一个关联结构,给出了其为1 1/2-设计的一个充要条件.另外,利用此关联结构得到了一个局部有向强正则图和LDPC码,并确定了它们的一些参数.
Projective geometry over finite fields is a large family of finite geometry. The structure of it has been well studied. In this paper, we give an incidence structure using fiats of projective space and present a sufficient and necessary condition of the structure to be a 1 1/2-design. In addition, a local directed strongly regular graph is studied and the parameters of some special LDPC codes based on this structure are also determined.