Coset Construction for Subspace Codes

Abstract

One of the main problems of the research area of network coding is to compute good lower and upper bounds of the achievable cardinality of so-called subspace codes in $\operatorname{PG}(n,q)$, i.e., the set of subspaces of $\mathbb{F}_q^n$, for a given minimal distance. Here we generalize a construction of Etzion and Silberstein to a wide range of parameters. This construction, named coset construction, improves or attains several of the previously best-known subspace code sizes and attains the MRD bound for an infinite family of parameters.