Supplementary difference sets and Jacobi sums

Let 4 = ef + 1 be an odd prime power and C,, 1 =Z i =S e 1, be cyclotomic classes of the eth power residues in F = GF(q). Let Ai with #A, = ujr 1 =~i Sn, be non-empty subsets of Q={O,l,..., e-l}andletD,=U,,,, C,, 1s i s n. Here we prove that D,, . . , D,, become n {q:uJ, ulf, . , uf; A} supplementary difference sets if and only if the following equations… CONTINUE READING