New extended sidon spaces with dimension k+1

Abstract In recent years, Sidon spaces have gained great popularity and applications in various fields such as multi-antenna communication systems, distributed storage systems, multimedia transmission, and network coding. With our further research into this field, it becomes evident that Sidon spaces are crucial in the field of constructing cyclic subspace codes. Currently, lots of papers focuse on how to construct Sidon spaces. Researchers find that through using the roots of irreducible polynomials and primitive elements over finite fields, we can sucessfully construct them. Based on the significant research conducted by previous scholars, we obtain several Sidon spaces which have new cardinality. Moreover, these Sidon spaces is beneficial to help us obtain better-performance subspace codes.