Abstract
Aq-nary error-correcting code withN = q^{k}code words of lengthn = k + rcan have no greater minimum distancedthanr+1. The class of codes for whichd = r+1is 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 ofq, k, andr.

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