New constructions of cyclic subspace codes via variants of Sidon spaces

Cyclic subspace codes, also known as cyclic constant dimension codes, play an important role in random network coding. A key challenge in classical coding theory is designing larger cyclic subspace codes with a given optimal minimum distance. This paper focuses on constructing large optimal cyclic subspace codes making use of variants of the Sidon spaces introduced by Roth [IEEE Trans. Inform. Theory 64 (6) 2018: 4412-4422] and Feng [Discrete Math. 344 (4) 2021: 112273]. We first investigate several variants of Sidon spaces and then utilize these spaces to explore new constructions of cyclic subspace codes. Our results show that these constructions yield larger codes while maintaining the optimal minimum distance, thereby establishing a new lower bound for cyclic subspace codes.