正交表行关系的研究

A RESEARCH ON THE RELATION BETWEEN ROWS OF ORTHOGONAL ARRAYS

研究正交阵列行之间的关系,这在以前是被忽略的。文中将 Hamming 距离引进正交阵列后,我们对正交阵列行之间的关系有了新认识,给出了两个定理。基于这两个定理,得出了一个完备型或 Hadamard 型正交阵列导出 BIB 设计或 PBIB设计的方法。文中涉及的主要理论有群论,伽罗华域,模代数和线性代数。

This paper deals with the relation between rows of orthogonal arrays,which was overlooked before.After introducing Hamming Distance to orthogonal arrays,we got a new idea of how the rows relate in an orthogonal array.Two theorems have been proved. Based on the two theorems,a method of deriving BIB and PBIB designs from a complete orthogonal array or an Hadamard orthogonal array has been got.The main means used in the paper are group theory,galois field,module algebra and linear algebra.