Sets in image with distinct sums of pairs Original Research Article

A subset S={s1,…,sk} of an abelian group G is called an St-set of size k if all sums of t different elements in S are distinct. A function with applications in coding theory, vγ(k) denotes the order of the smallest cyclic group in which an S2-set of size k exists. A lower bound for vγ(k) is given in this study, and exact values of vγ(k) are obtained for k⩽15. For the related problem in which all sums of any two, not necessarily distinct, elements in S are required to be different, values of the corresponding function vδ(k) for each k⩽14 are given.