Subsets in Linear Spaces over the Finite Field F_3 Uniquely Determined by Their Pairwise Sums Collection

摘要

Let F-3(n) be an n-dimensional linear space over the finite field F-3. Let A = {a(1), a(2),..., a(N)} be a set in F-3(n) and A + A be the collection of sums of pairs of distinct elements in A. It is said, that A is uniquely determined by A + A if for any B F-3(n) such that |A| = |B| and A + A = B + B it follows that A = B. In this paper, we find those values of N for which any set A subset of F-3(n) containing N elements is determined uniquely by A + A.