Two new constructions of cyclic subspace codes via Sidon spaces

The article delves into the construction of cyclic subspace codes, specifically focusing on constant dimension codes (CDCs) with large minimum distances and numerous codewords. By leveraging Sidon spaces, the authors present two novel constructions that enhance the performance of cyclic CDCs. The first construction provides a cyclic -CDC with a size of , while the second construction achieves a cyclic -CDC with a size of . These constructions not only increase the number of codewords but also optimize the minimum distance, bringing the code sizes closer to the sphere-packing bound. The paper concludes by highlighting the potential for further research in constructing new Sidon spaces and cyclic subspace codes with even more codewords.