Full rank distance codes and optimal STBC for BPSK modulation

Viewing the codewords of an [n, k] linear code over a field F(q/sup m/) as m/spl times/n matrices over F/sub q/ by expanding each entry of the codeword with respect to an F/sub q/-basis of F(q/sup m/), the rank weight of a codeword is the rank over F/sub q/ of the corresponding matrix and the rank of the code is the minimum rank weight among all non-zero codewords. For m/spl ges/n-k+1, codes with maximum possible rank distance, called maximum rank distance (MRD) codes have been studied previously. We study codes with maximum possible rank distance for the cases m/spl les/n-k+1, calling them full rank distance (FRD) codes. Generator matrices of FRD codes are characterized.