On cardinality of network subspace codes 1

We analyze properties of different subspace network codes. Our study includes Silva-Koetter-Kshishang codes (SKK-codes), multicomponent codes with zero prefix (Gabidulin-Bossert codes), codes based on combinatorial block designs, Etzion-Silberstein codes (E-S codes) based on Ferrer’s diagrams, and codes which use greedy search algorithm and restricted rank codes. We calculate cardinality values of these codes for different parameters and compare actual cardinality with the upper bound of subspace codes. The ratio of the actual cardinality to the upper bound is called code efficiency. It is shown that multicomponent codes have greater efficiency than SKK-codes for all parameters. In cases of minimal and maximum code distances the upper bound of cardinality is attained for some codes under consideration.