OFFSET
1,1
COMMENTS
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.
Graphs of APN functions from GF(2)^n to GF(2)^m are Sidon sets (as subsets of GF(2)^(n+m)).
LINKS
Ingo Czerwinski and Alexander Pott, Sidon sets, sum-free sets and linear codes, arXiv:2304.07906 [math.CO], 2023-2024, Prop. 2.7 and Table 2.
Ingo Czerwinski and Alexander Pott, Sidon sets, sum-free sets and linear codes, Advances in Mathematics of Communications, 2024, 18(2): 549-566.
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Aleksei Udovenko, Mar 07 2026
STATUS
approved
