Large constant dimension codes and lexicodes

Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the code words in such a code are subspaces of Fⁿ_q with a given dimension. A computer search for large constant dimension codes is usually in efficient since the search space domain is extremely large. Even so, we found that some constant dimension lexicodes are larger than other known codes. We show how to make the computer search more efficient. In this context we present a formula for the computation of the distance between two subspaces, not necessarily of the same dimension.