31 research outputs found
Strongly Regular Graphs From Unions of Cyclotomic Classes
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 parameters.Comment: 17 pages; to appear in J. Combin. Theory (B
Cyclotomic Constructions of Skew Hadamard Difference Sets
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
, where is a prime and a positive integer. Our main tools
are index 2 Gauss sums, instead of cyclotomic numbers.Comment: 15 pages; corrected a few typos; to appear in J. Combin. Theory (A