Large optimal cyclic subspace codes

Constant dimension codes, a specialized subclass of subspace codes, have garnered significant attention in recent years due to their applications in random network coding. Among these codes, large cyclic constant dimension codes, endowed with optimal minimum distance, offer efficient solutions for encoding and decoding algorithms. This paper is dedicated to the design of cyclic constant dimension codes that achieve the dual goals: maximizing code size while maintaining optimal minimum distance. We first explore a new form of Sidon spaces and employ this new form to construct several families of cyclic subspace codes. Our codes have optimal minimum distances and have more codewords than previous constructions in the literature.