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A q -nary error-correcting code with N = q^k code words of length n = k + r can have no greater minimum distance d than r+1. The class of codes for which d = r+1 is studied first in general, then with the restriction that the codes be linear. Examples and construction methods are given to show that these codes exist for a number of values of q, k, and r.
R. C. Singleton (Wed,) studied this question.
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