This is the first exposition of the theory of quasi-symmetric designs, that is, combinatorial designs with at most two block intersection numbers. The authors aim to bring out the interaction among designs, finite geometries, and strongly regular graphs. The book starts with basic, classical material on designs and strongly regular graphs and continues with a discussion of some important results on quasi-symmetric designs. The later chapters include a combinatorial construction of the Witt designs from the projective plane of order four, recent results dealing with a structural study of designs resulting from Cameron's classification theory on extensions of symmetric designs, and results on the classification problem of quasi-symmetric designs. The final chapter presents connections to coding theory.
Author(s): Mohan S. Shrikhande, Sharad S. Sane
Series: London Mathematical Society Lecture Note Series
Publisher: CUP
Year: 1991
Language: English
Pages: 242
Cover......Page 1
Quasi-symmetric Designs......Page 4
Goto 4 /FitH 555521414075......Page 5
Contents......Page 8
Preface......Page 10
Acknowledgments......Page 17
I. Basic results from designs......Page 18
II. Strongly regular graphs and partial geometries......Page 34
III. Basic results on quasi-symmetric designs......Page 51
IV. Some configurations related to strongly regular graphs and quasi-symmetric designs......Page 66
V. Strongly regular graphs with strongly regular decompositions......Page 99
VI. The Witt designs......Page 116
VII. Extensions of symmetric designs......Page 139
VIII. Quasi-symmetric 2-designs......Page 158
IX. Towards a classification of quasi-symmetric 3-designs......Page 191
X. Codes and quasi-symmetric designs......Page 209
References......Page 224
Index......Page 239
