Duality theory for space-time codes over finite fields
We further the study of the duality theory of linear space-time codes over finite fields by showing that the only finite linear "omnibus" codes (defined herein) with a duality theory are the column distance codes and the rank codes. We introduce weight enumerators for both these codes and show that they have MacWilliams-type functional equations relating them to the weight enumerators of their duals. We also show that the complete weight enumerator for finite linear sum-of-ranks codes satisfies such a functional equation. We produce an analogue of Gleason's Theorem for formally self-dual linear finite rank codes. Finally, we relate the duality matrices of n x n linear finite rank codes and length n vector codes under the Hamming metric.
space-time codes finite fields linear codes