2 research outputs found
A feasibility approach for constructing combinatorial designs of circulant type
In this work, we propose an optimization approach for constructing various
classes of circulant combinatorial designs that can be defined in terms of
autocorrelations. The problem is formulated as a so-called feasibility problem
having three sets, to which the Douglas-Rachford projection algorithm is
applied. The approach is illustrated on three different classes of circulant
combinatorial designs: circulant weighing matrices, D-optimal matrices, and
Hadamard matrices with two circulant cores. Furthermore, we explicitly
construct two new circulant weighing matrices, a and a
, whose existence was previously marked as unresolved in the most
recent version of Strassler's table
Paley type group schemes from cyclotomic classes and Arasu-Dillon-Player difference sets
In this paper, we present constructions of abelian Paley type group schemes
by using multiplicative characters of finite fields and Arasu-Dillon-Player
difference sets. The constructions produce many new Paley type group schemes
that were previous unknown in our classification of Paley type group schemes in
finite fields of small orders