Large cyclic subspace codes based on the generalized Sidon spaces
Yongfeng Niu, Yu Li, Yuye Feng, Lingling Wu · Advances in Mathematics of Communications · 2025
In recent years, the influence of cyclic subspace codes has significantly grown in the field of random network coding, making it a highly noteworthy research focus. Crucially, we have gained a profound understanding that Sidon spaces serve as the indispensable cornerstone for constructing cyclic subspace codes. In this paper, we leverage the roots of irreducible polynomials and primitive elements over finite fields to construct Sidon spaces. Based on this, we successfully construct Sidon spaces with a set of novel parameters. On this foundation, we have further constructed cyclic subspace codes that are larger in size. In summary, by thoroughly studying the achievements of previous researchers, we have successfully extended the construction of Sidon spaces and obtained cyclic subspace codes with larger size.