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Viewing the codewords of an [n, k] linear code over a field F(qm) as m×n matrices over Fq by expanding each entry of the codeword with respect to an Fq-basis of F(qm), the rank weight of a codeword is the rank over Fq of the corresponding matrix and the rank of the code is the minimum rank weight among all non-zero codewords. For m≥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≤n-k+1, calling them full rank distance (FRD) codes. Generator matrices of FRD codes are characterized.