Let V be a k-dimensional subspace of \({{\mathbb {F}}}_{q^n}\). Define \(a{{\mathbb {F}}}_q=\{a\lambda :\lambda \in {{\mathbb {F}}}_q\}\). We call V the Sidon space if any nonzero a, b, c and \(d\in V\) such that \(ab=cd\), then \(\{a{{\mathbb {F}}}_q,b{{\mathbb {F}}}_q\}=\{c{{\mathbb {F}}}_q,d{{\mathbb {F}}}_q\}\). We first provide the new results for high-dimensional Sidon spaces by using the direct sum of two small-dimensional Sidon spaces. Besides, we develop and generalize the constructions of cyclic subspace codes presented in Niu (Discret Math 343(5):111788, 2020) and Feng (Discret Math 344(4):112273, 2021), and further obtain several large ones without changing minimum distance through combining the orbits of distinct Sidon spaces.

令V为\({{\mathbb {F}}}_{q^n}\)的k维子空间。定义\(a{{\mathbb {F}}}_q=\{a\lambda :\lambda \in {{\mathbb {F}}}_q\}\)。如果任何非零a、  b、  c和\(d\in V\)满足\(ab=cd\)，则称V为Sidon 空间，则\(\{a{{\mathbb {F}}}_q, b{{\mathbb {F}}}_q\}=\{c{{\mathbb {F}}}_q,d{{\mathbb {F}}}_q\}\）. 我们首先通过使用两个小维 Sidon 空间的直接和来提供高维 Sidon 空间的新结果。此外，我们开发和推广了 Niu (Discret Math 343(5):111788, 2020) 和 Feng (Discret Math 344(4):112273, 2021) 中提出的循环子空间码的构造，并进一步获得了几个大的而不改变通过组合不同西顿空间的轨道的最小距离。