This IMA Volume in Mathematics and its Applications Coding Theory and Design Theory Part I: Coding 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 qOn a problem of Combinatoricsq, 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 R. C. Bose's 1939 Annals of Eugenics paper, qOn the construction of balanced incomplete block designsq. Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R. C. Bose's 1947 Sankhya paper qMathematical theory of the symmetrical factorial designsq.Thus the weight-distributions of the code C(Q3-20F)) for the two cases - Q21a1 elliptic and Q21a1 hyperbolic are given below. (7.2) - Q2ta1elliptic Q2ta1. hyperbolic weight frequency : weight frequency 0 1 0 1 s2t-3 a st-1 + st-2 (s a 1)s ?-? s2t-3 + st-1 ... BoSE, R.C., On the application of finite projective geometry for deriving a certain series of balanced Kirkman arrangements, Calcutta Math. Soc. Goldenanbsp;...

Title | : | Coding Theory and Design Theory |

Author | : | Dijen Ray-Chaudhuri |

Publisher | : | Springer Science & Business Media - 2012-12-06 |

You must register with us as either a Registered User before you can Download this Book. You'll be greeted by a simple sign-up page.

Once you have finished the sign-up process, you will be redirected to your download Book page.

`1.`Register a free 1 month Trial Account.`2.`Download as many books as you like (Personal use)`3.`Cancel the membership at any time if not satisfied.