Some Matrix Constructions of Group Divisible Designs

• Main Authors: Cheng Szu-En, 鄭斯恩
• Other Authors: E. T. Tan
• Format: Others
• Language: en_US
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/06798938925518826431

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.