| Summary: | 碩士 === 國立政治大學 === 應用數學研究所 === 81 === 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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