On Rosenbloom and Tsfasman's generalization of the Hamming space

Rosenbloom and Tsfasman introduced a generalization of the Hamming metric, motivated by a model of information transmission over parallel channels, and obtained bounds on the cardinality of codes in the induced finite metric space. In the present paper, some new bounds are given and the analogue of the Plotkin bound is improved. Furthermore, the following problem together with some results is presented: which are the parameters such that there exist codes meeting the Singleton bound in the new space? The binary case is solved.