Some New Difference Sets

Abstract

A difference set is a set D = {d1, d2, … , dk] of k distinct residues modulo v such that each non-zero residue occurs the same number of times among the k(k — 1) differences di — dj, i ≠ j. If λ is the number of times each difference occurs, then(1)When we wish to emphasize the particular values of v, k, and λ involved we will call such a set a (v, k, λ) difference set. Another (v, k, λ) difference set E = {e1, e2, … ek} is said to be equivalent to the original one if there exist a and t such that (t, v) = 1 and E = {a + td1, … , a + tdk}. If t = 1 we will call the set E a slide of the set D. If D = E, then t is called a multiplier of D.