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 loosing the Sidon property, up to dimension 6 and give all possible sizes for dimension 7 and 8 determined by computer calculations.

翻译：寻找$\mathbb{F}_2^t$中Sidon集的最大规模已持续研究超过40年。为解决该问题，我们回顾了和-free Sidon集与最小距离≥5的线性码之间的一一对应关系。关于编码理论的主要贡献是基于Johnson界的锐化，提出了最小距离为5的线性码的新的不存在性结论。这一结果在Sidon集方面改进了其最大规模的一般上界。此外，我们刻画了维度至多为6的极大Sidon集（即无法通过添加元素来保持Sidon性质的集合），并通过计算机计算给出了维度7与8的所有可能规模。