Cardinality of Subspace Multicomponent Codes

This paper is devoted to multicomponent subspace codes with zero prefix (MZP). The construction is described. The codes are divided into two parts. The first part contains the codes which code distance is not maximal. The second part contains of the codes with maximal code distance, so called partial spreads. It connects with different ways to estimate the upper bounds of cardinality. Cardinality for codes is calculated for different parameters. The obtained values are compared with the corresponding upper bounds. It is shown that the cardinality of the codes from the first part does not coincides with the upper bound. The cardinality of the partial spreads coincides or almost coincides with the upper bound. It depends on code dimension. By definition, efficiency is defined as ratio of the cardinality of the code for given parameters to the upper bound at the same parameters.