WEIGHT ENUMERATORS AND A MACWILLIAMS-TYPE IDENTITY FOR SPACE-TIME RANK CODES OVER FINITE FIELDS

摘要

Several authors have considered the analogue of space-time codes over finite fields, usually taking the distance between two matrices as the rank of their difference. We introduce a weight enumerator for these "finite rank codes," and show that there is a MacWilliams-type identity connecting the weight enumerator of a linear finite rank code to that of its dual. We do so with a proof of sufficient generality that it simultaneously derives the classical MacWilliams identity for linear block codes. Finally, we demonstrate a close relationship between the MacWilliams identity for linear finite rank codes and that for linear block codes.