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This paper gives two new bounds for the code word length n which is required to obtain a binary group code of order 2 k with mutual distance d between code words. These bounds are compared with previously known bounds, and are shown to improve upon them for certain ranges of k and d. Values of k and d are given for which one of these bounds can actually be achieved; in such cases, the structure of the resulting codes is shown to satisfy a certain condition.
James H. Griesmer (Tue,) studied this question.