منابع مشابه
A Brief Survey of Difference Sets, Partial Difference Sets, and Relative Difference Sets
Difference sets, partial difference sets, and relative difference sets are algebraic structures with combinatorial applications. The purpose of this paper is to give the reader definitions and basic examples of these sets, as well describe their connections to some other well-known combinatorial objects. We will conclude with some examples that illustrate how character theory can be used to pro...
متن کاملConstructions of Partial Difference Sets and Relative Difference Sets on /7-groups
By using some finite local rings, we construct some new partial difference sets and relative difference sets on ^-groups where p is any prime. When p = 2, some of the partial difference sets constructed are reversible difference sets which include Dillon's difference sets.
متن کاملRelative Difference Sets Partitioned by Cosets
We explore classical (relative) difference sets intersected with the cosets of a subgroup of small index. The intersection sizes are governed by quadratic Diophantine equations. Developing the intersections in the subgroup yields an interesting class of group divisible designs. From this and the Bose-Shrikhande-Parker construction, we obtain some new sets of mutually orthogonal latin squares. W...
متن کاملSemifields, Relative Difference Sets, and Bent Functions
Recently, the interest in semifields has increased due to the discovery of several new families and progress in the classification problem. Commutative semifields play an important role since they are equivalent to certain planar functions (in the case of odd characteristic) and to modified planar functions in even characteristic. Similarly, commutative semifields are equivalent to relative dif...
متن کاملTwo Generalized Constructions of Relative Difference Sets
We give two generalizations of some known constructions of relative difference sets. The first one is a generalization of a construction of RDS by Chen, Ray-Chaudhuri and Xiang using the Galois ring GR(4,m). The second one generalizes a construction of RDS by Ma and Schmidt from the setting of chain rings to a setting of more general rings.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2003
ISSN: 0097-3165
DOI: 10.1016/s0097-3165(02)00013-4