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：在$\mathbb{F}_2^t$中寻找Sidon集的最大规模是四十多年来持续受到关注的研究课题。为攻克此问题，我们回顾了无和Sidon集与最小距离大于等于5的线性码之间的一一对应关系。我们在编码方面的主要贡献是基于Johnson界的改进，得到了关于最小距离为5的线性码的一个新的非存在性结果。这在Sidon集方面改进了关于Sidon集最大规模的一般上界。此外，我们刻画了直至维度6的极大Sidon集（即那些无法通过添加元素而不破坏Sidon性质的集合），并通过计算确定了维度7和8的所有可能规模。