New Constructions of Sidon Spaces and Cyclic Subspace Codes

Abstract

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