New Constructions of Sidon Spaces and Cyclic Subspace Codes

Sidon space is an important tool for constructing cyclic subspace codes. In this letter, we construct some spaces by using primitive elements and the roots of irreducible polynomials over finite fields. Let q be a prime power, k, m, n three positive integers $\rho= \lceil \frac{m}{2k}\rceil-1$, $\theta= \frac{n}{2m}\rceil-1$. Based on these union spaces, new codes with size $\frac{3(q^{n}-1)}{q-1}$ $\frac{\theta\rho q^{k}(q^{n}-1)}{q-1}$ are obtained. The lager compared to known constructions from [14] [10].