63 research outputs found
Frame difference families and resolvable balanced incomplete block designs
Frame difference families, which can be obtained via a careful use of
cyclotomic conditions attached to strong difference families, play an important
role in direct constructions for resolvable balanced incomplete block designs.
We establish asymptotic existences for several classes of frame difference
families. As corollaries new infinite families of 1-rotational
-RBIBDs over are
derived, and the existence of -RBIBDs is discussed. We construct
-RBIBDs for , whose
existence were previously in doubt. As applications, we establish asymptotic
existences for an infinite family of optimal constant composition codes and an
infinite family of strictly optimal frequency hopping sequences.Comment: arXiv admin note: text overlap with arXiv:1702.0750
New -designs from strong difference families
Strong difference families are an interesting class of discrete structures
which can be used to derive relative difference families. Relative difference
families are closely related to -designs, and have applications in
constructions for many significant codes, such as optical orthogonal codes and
optical orthogonal signature pattern codes. In this paper, with a careful use
of cyclotomic conditions attached to strong difference families, we improve the
lower bound on the asymptotic existence results of -DFs for .
We improve Buratti's existence results for - designs and
- designs, and establish the existence of seven new
- designs for
,
.Comment: Version 1 is named "Improved cyclotomic conditions leading to new
2-designs: the use of strong difference families". Major revision according
to the referees' comment
Partitionable sets, almost partitionable sets and their applications
This paper introduces almost partitionable sets to generalize the known
concept of partitionable sets. These notions provide a unified frame to
construct -cyclic patterned starter whist tournaments and cyclic
balanced sampling plans excluding contiguous units. The existences of
partitionable sets and almost partitionable sets are investigated. As an
application, a large number of maximum or maximal optical orthogonal codes are
constructed. These maximal optical orthogonal codes fail to be maximum for just
one codeword
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