Two new constructions of cyclic subspace codes via Sidon spaces

A subspace of a finite field is called a Sidon space if the product of any two of its nonzero elements is unique up to a scalar multiplier from the base field. Sidon spaces, introduced by Roth et al. in (IEEE Trans Inf Theory 64(6):4412–4422, 2018), have a close connection with optimal full-length orbit codes. In this paper, we will construct several families of large cyclic subspace codes based on the two kinds of Sidon spaces. These new codes have more codewords than the previous constructions in the literature without reducing minimum distance. In particular, in the case of \(n=4k\) $n=4k$ , the size of our resulting code is within a factor of \(\frac{1}{2}+o_{k}(1)\) $\frac{1}{2}+o_k(1)$ of the sphere-packing bound as k goes to infinity.