Sidon sets, sum-free sets and linear codes
Ingo Czerwinski, Alexander Pott · Advances in Mathematics of Communications · 2023
Finding the maximum size of a Sidon set in $ \mathbb{F}_2^{{t}} $ is of research interest for more than 40 years. In order to tackle this problem we recall a one-to-one correspondence between sum-free Sidon sets and linear codes with minimum distance greater or equal 5. Our main contribution about codes is a new non-existence result for linear codes with minimum distance 5 based on a sharpening of the Johnson bound. This gives, on the Sidon set side, an improvement of the general upper bound for the maximum size of a Sidon set. Additionally, we characterise maximal Sidon sets, that are those Sidon sets which can not be extended by adding elements without losing the Sidon property, up to dimension 6 and give all possible sizes for dimension 7 and 8 determined by computer calculations.