Subsets in Linear Spaces over the Finite Field F3 Uniquely Determined by Their Pairwise Sums Collection

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...

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Bibliographic Details
Published inJournal of contemporary mathematical analysis Vol. 54; no. 2; pp. 65 - 70
Main Author Sargsyan, D.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.03.2019
Subjects
Algebra
Mathematics
Mathematics and Statistics
uniqueness
11B75
Pairs of distinct elements
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Summary: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 ⊂ F 3 n containing N elements is determined uniquely by A + A .
ISSN:1068-3623
1934-9416
DOI:10.3103/S106836231902002X