Subspace mixed dimension codes based on Gabidulin-Bossert multicomponent codes

In this work, subspace mixed dimension codes based on Gabidulin-Bossert multicomponent codes are constructed and their main characteristics are analyzed. An algorithm for constructing a family of such codes is described. The optimal parameters for the highest cardinality are found. Using a three component code, a simple code of the highest cardinality with a large line of subspace distances is constructed. It is shown that at large distances the cardinality of our code practically coincides with the known lower bound. Comparative cardinality estimations for constant and mixed dimension subspace codes showed that cardinality of mixed dimension codes is exponentially higher than cardinality of constant dimension codes. Examples are given.