Title: Subspace Polynomials and Cyclic Subspace Codes

 

Abstract: Subspace codes are collections of subspaces of the finite vector space $\mathbb{F}^n_q$ under the subspace metric. Of particular interest due to their efficient encoding/decoding algorithms are constant dimension cyclic codes where each codeword is a subspace of the same dimension and which are invariant under an action of $\mathbb{F}^{*}_{q^n}$.  We will see how to represent subspace codes using particular polynomials and deduce properties of the codes from the structure of these polynomials based on the work of Ben-Sasson et. al. in 2016. Using these results, we will give a construction of a constant dimension cyclic code containing multiple orbits under the $\mathbb{F}^{*}_{q^n}$ action with highest possible subspace distance.