Sets in ?n ? n with distinct sums of pairs ?
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, v?(k) denotes the order of the smallest cyclic group in which an S2-set of size k exists. A lower bound for v?(k) is given in this study, and exact values of v?(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 v?(k) for each k?14 are given.
additive base backtrack search difference set packing