Cyclic subspace codes, as a specific subclass of subspace codes, have garnered significant attention in recent years, primarily due to their application in random network coding. Recently, by using the connection with Sidon spaces, progressively larger codes have been obtained. Let m, n, t, k be positive integers such that k|n|m. Let \(\mathcal {G}_q(m,t)\) denote the set of all \({\mathbb F}_q\) -subspaces of \({\mathbb F}_{q^m}\) . In this paper, we investigate the construction of optimal multi-orbit cyclic subspace codes in the Grassmannian space \(\mathcal {G}_q(m,t)\) using the direct sum of Sidon spaces, where t is not necessarily a divisor of m. Previous works Li [Des Codes Cryptogr 91:1193–1207, 2023) and Castello [J Algebr Comb 58:1299–1329, 2023) studied single-orbit cyclic subspace codes in \(\mathcal {G}_q(m,k_1+k_2)\) via direct sum methods, where \(k_1,k_2\le n\) and \(t=k_1+k_2\) . Applying the direct sum of Sidon spaces, we further explore their results and establish sufficient conditions for optimal multi-orbit cyclic subspace codes in \(\mathcal {G}_q(m,k_1 + k_2)\) . Then, by carefully selecting Sidon spaces in \(\mathcal {G}_q(m,2k)\) , we construct a large class of cyclic subspace codes with cardinality \((q^k-1)(q^m-1)\) and minimum distance \(4k-2\) , where \(2k\not \mid m\) . Our main contribution is to address the problem of constructing optimal multi-orbit cyclic subspace codes in \(\mathcal {G}_q(m,t)\) without requiring t to divide m, improving existing approaches. We provide a new direction for studying optimal multi-orbit cyclic subspace codes in \(\mathcal {G}_q(m,t)\) with large cardinality and it implies the potential for constructing even larger codes where the subspace dimension does not necessarily divide the ambient dimension.
