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%I #14 Mar 25 2026 23:13:20
%S 2,3,4,6,7,9,12,18,24,34
%N Maximum size of a subset of GF(2)^n being a Sidon set.
%C A subset A of an abelian group G is a Sidon set if the twofold sums of elements in A are pairwise distinct. For G the additive group of GF(2)^n, equivalently, A is a Sidon set if there exist no four distinct elements in A summing to zero.
%C Graphs of APN functions from GF(2)^n to GF(2)^m are Sidon sets (as subsets of GF(2)^(n+m)).
%H Ingo Czerwinski and Alexander Pott, <a href="https://arxiv.org/abs/2304.07906">Sidon sets, sum-free sets and linear codes</a>, arXiv:2304.07906 [math.CO], 2023-2024, Prop. 2.7 and Table 2.
%H Ingo Czerwinski and Alexander Pott, <a href="https://doi.org/10.3934/amc.2023054">Sidon sets, sum-free sets and linear codes</a>, Advances in Mathematics of Communications, 2024, 18(2): 549-566.
%e a(2) = 3 because 00, 01, 11 is a Sidon set in GF(2)^2, but the (only other possible) element 10, cannot be added to this set because 00+01+10+11 = 00.
%K nonn,hard,more
%O 1,1
%A _Aleksei Udovenko_, Mar 07 2026