在本篇論文中我們使用矩陣來建構可分組設計(GDD), 我們列出了兩種型

式的建構, 第一種 -- 起因於 W.H. Haemers -- A .crtimes. J + I

.crtimes. D, 利用此種建構我們將所有符合 r - .lambda.1 = 1 的

(m,n,k,.lambda.1,.lambda.2) GDD 分成三類: (i) A=0 或 J-I, (ii)

A 為 .mu. - .lambda. = 1 強則圖的鄰接矩陣, (iii) J-2A 為斜對稱

矩陣的核心。第二種型式為 A .crtimes. D + .Abar .crtimes. .Dbar

,此種方法可以建構出 b=4(r-.lambda.2) 的正規和半正規 GDD 。另外在

論文中, 我們研究在這些建構中出現的相關題目。

In this thesis we use matrices to construct group divisible

designs (GDDs). We list two type of constructions, the first

type is -- due to W.H. Heamers -- A .crtimes. J + I .crtimes.

D and use this construction we classify all the (m,n,k,.

lambda.1, .lambda.2) GDD with r - .lambda.1 = 1 in three

classes according to (i) A = 0 or J-I, (ii) A is the adjacency

matrix of a strongly regular graph with .mu. - .lambda. = 1,

(iii) J - 2A is the core of a skew-symmetric Hadamard matrix.

The second type is A .crtimes. D + .Abar .crtimes. .Dbar ,

this type can construct many regular and semi-regular GDDs with

b=4(r-.lambda.2). In the thesis we investigate related topics

that occur in these constructions.

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