The Existence Of Some Classes Of Almost Difference Families

Almost difference families(ADFs) are an immediate generalization of almost differencesets(ADSs). In this paper, we establish a number of infinite classes of ADFs by some con-structive techniques. Especially, we employ the theory of cyclotomy and Weil's theorem toobtain a (q, 3,1, (q-1)/2)-ADF and a (q, 4, 1, (4(q-1))/5)-ADF in GF(q). Difference matrices areused to construct recursively some new ADFs in the additive of group GF(p)⊕GF(q). Acomposite construction method of ADFs is also presented.