LAUSR

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 ${ \mathcal {P}_{q}(n)}$ , 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 maximum-rank distance bound for an infinite family of parameters.