Related papers: Skew Hadamard difference sets from cyclotomic stro…
In this paper, we give a construction of strongly regular Cayley graphs and a construction of skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and they generalize the constructions…
In this paper, we give constructions of strongly regular Cayley graphs and skew Hadamard difference sets. Both constructions are based on choosing cyclotomic classes in finite fields, and our results generalize ten of the eleven sporadic…
We revisit the old idea of constructing difference sets from cyclotomic classes. Two constructions of skew Hadamard difference sets are given in the additive groups of finite fields using unions of cyclotomic classes of order $N=2p_1^m$,…
In this paper we construct exponentionally many non-isomorphic skew Hadamard difference sets over an elementary abelian group of order $q^3$.
Using cyclotomic classes of order twelve for certain finite fields, we construct an infinite family of almost difference sets and normally regular graphs applying the theory of cyclotomy. We show that in each of these fields neither the…
We give a new construction of difference families generalizing Szekeres's difference families \cite{Sze}. As an immediate consequence, we obtain some new examples of difference families with several blocks in multiplicative subgroups of…
In this paper, we generalize classical constructions of skew Hadamard difference families with two or four blocks in the additive groups of finite fields given by Szekeres (1969, 1971), Whiteman (1971) and Wallis-Whiteman (1972). In…
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…
Recently, Feng and Xiang \cite{FX113} found a new construction of skew Hadamard difference sets in elementary abelian groups. In this paper, we introduce a new invariant for equivalence of skew Hadamard difference sets, namely triple…
We construct a skew-Hadamard matrix of order 1252 = 2(5^4 + 1) using a bordered skew-Hadamard difference family over GF(5^4), with blocks given as unions of cyclotomic classes of order N = 16. This order has been reported as missing in some…
Using a class of permutation polynomials of $F_{3^{2h+1}}$ obtained from the Ree-Tits symplectic spreads in $PG(3,3^{2h+1})$, we construct a family of skew Hadamard difference sets in the additive group of $F_{3^{2h+1}}$. With the help of a…
We construct several difference families on cyclic groups of orders 47 and 97, and use them to construct skew-Hadamard matrices of orders 188 and 388. Such difference families and matrices are constructed here for the first time. The…
We give two constructions of strongly regular Cayley graphs on finite fields $\F_q$ by using union of cyclotomic classes and index 2 Gauss sums. In particular, we obtain twelve infinite families of strongly regular graphs with new…
We single out a class of difference families which is widely used in some constructions of Hadamard matrices and which we call Goethals--Seidel (GS) difference families. They consist of four subsets (base blocks) of a finite abelian group…
In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…
First we give an overview of the known supplementary difference sets (SDS) (A_i), i=1..4, with parameters (n;k_i;d), where k_i=|A_i| and each A_i is either symmetric or skew and k_1 + ... + k_4 = n + d. Five new Williamson matrices over the…
This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…
Strong external difference family (SEDF) and its generalizations GSEDF, BGSEDF in a finite abelian group $G$ are combinatorial designs raised by Paterson and Stinson [7] in 2016 and have applications in communication theory to construct…
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…
We give a construction of strongly regular Cayley graphs on finite fields $\F_q$ by using union of cyclotomic classes and index 4 Gauss sums. In particular, we obtain two infinite families of strongly regular graphs with new parameters.