Coding Theory and Design Theory: Design theory
These books are based on the proceedings of a workshop which was an integral part of the 1987-88 IMA program on Applied Combinatorics. Coding Theory and Design theory are areas of combinatorics which found rich applications of algebraic structures and are closely interconnected. Coding theory has developed into a rich and beautiful example of abstract sophisticated mathematics being applied successfully to solve real-life problems of communication.
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Recent results on difference sets
Automorphism groups of block structures with
Families of codes with few distinct weights from singular
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1-factorizations 2-groups 2-idempotent abelian group affine plane algebraic association scheme automorphism group balanced incomplete block BIB designs BIBD Bruck coefficients columns combinatorial conjecture construction contains corresponding cyclic defined definition denote Design Theory element elementary abelian equivalent examples exists factorial experiment finite following result group G group of order Hadamard difference sets Hadamard matrices Hedayat Hence idempotent implies incidence matrix intersection numbers Jungnickel k-statistics Lemma Let G linear Math maximal MEP-1 plan multiplier mutually orthogonal Latin notation Note number of blocks OA(t obtain orbits ordinary points orthogonal Latin squares pair parallel classes parameters partition permutation plane of order polynomial prime power problem projective planes Proof proved quasigroup RBIBD resolution classes roots of unity rows semibiplane Shrikhande special points Statist strongly regular graph subgroup subset support sizes Suppose Sylow p-subgroup symmetric t-designs Theorem Theorem 4.1 translation nets transversal designs treatments of weight wreath product