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Coding Theory and Design Theory - Part II Design Theory (Paperback, Softcover reprint of the original 1st ed. 1990)
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Coding Theory and Design Theory - Part II Design Theory (Paperback, Softcover reprint of the original 1st ed. 1990)
Series: The IMA Volumes in Mathematics and its Applications, 21
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This IMA Volume in Mathematics and its Applications Coding Theory
and Design Theory Part II: Design Theory is based on the
proceedings of a workshop which was an integral part of the 1987-88
IMA program on APPLIED COMBINATORICS. We are grateful to the
Scientific Committee: Victor Klee (Chairman), Daniel Kleitman,
Dijen Ray-Chaudhuri and Dennis Stanton for planning and
implementing an exciting and stimulating year long program. We
especially thank the Workshop Organizer, Dijen Ray-Chaudhuri, for
organizing a workshop which brought together many of the major
figures in a variety of research fields in which coding theory and
design theory are used. A vner Friedman Willard Miller, Jr. PREFACE
Coding Theory and Design Theory are areas of Combinatorics which
found rich applications of algebraic structures. Combinatorial
designs are generalizations of finite geometries. Probably, the
history of Design Theory begins with the 1847 pa per of Reverand T.
P. Kirkman "On a problem of Combinatorics," Cambridge and Dublin
Math. Journal. The great Statistician R. A. Fisher reinvented the
concept of combinatorial 2-design in the twentieth century.
Extensive application of alge braic structures for construction of
2-designs (balanced incomplete block designs) can be found in RC.
Bose's 1939 Annals of Eugenics paper, "On the construction of
balanced incomplete block designs." Coding Theory and Design Theory
are closely interconnected. Hamming codes can be found (in
disguise) in RC. Bose's 1947 Sankhya paper "Mathematical theory of
the symmetrical factorial designs.""
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