Comparative Characteristics of Constant and Mixed Dimension Subspace Codes

In this paper, constant and mixed dimension subspace codes based on multicomponent zero prefix codes are considered. Their cardinalities are estimated under the condition that the dimension of constant dimension code is equal to the minimum rank distance. Subject to this condition, cardinality of constant dimension code is equal to the upper bound. The algorithm for constructing mixed dimension codes with optimal parameters is described. It is shown that cardinality of mixed dimension codes is much higher than cardinality of constant dimension code at the same values of code words and the same subspace distance.