# Full Rank Distance Codes and Optimal STBC for BPSK Modulation

Manoj, KN and Rajan, Sundar B (2002) Full Rank Distance Codes and Optimal STBC for BPSK Modulation. In: IEEE International Symposium on Information Theory, 2002, June 30 - July 5,, Lausanne,Switzerland, p. 276.

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Viewing the codewords of an $[n,k]$ linear code over a field $F_{q^m}$ as ${m} X {n}$ matrices over $F_q$ by expanding each entry of the codeword with respect to an $F_q$ -basis of $F_{q^m}$, the rank weight of a codeword is the rank over $F_q$ of the corresponding matrix and the rank of the code is the minimum rank weight among all non-zero codewords. For ${m}\leq{n}-{k+1}$, 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 ${m}\leq{n}-{k+1}$, calling them full rank distance (FRD) codes. Generator matrices of FRD codes are characterized.