New constructions of Sidon spaces and large cyclic constant dimension codes

Sidon spaces initially were introduced by Bachoc, Serra, and Zémor as a tool to characterize multiplicative properties of subspaces and systematically were designed by Roth, Raviv, and Tamo utilizing some roots of irreducible polynomials over the finite fields. Roth, Raviv, and Tamo have also shown the relation between Sidon spaces and cyclic constant dimension codes and constructed several such codes with one or more orbits. In this paper, we survey the constructions of Sidon spaces with new parameters. Furthermore, we present a family of large cyclic subspace codes in which the code size exceeds the previous works.