Abstract
If the constraint length of a convolutional code is defined suitably, it is an obvious upper bound on the free distance of the code, and it is sometimes possible to find codes that meet this bound. It is proved here that the length of a rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/\nu q</tex> -ary code with this property is at most <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q\nu</tex> , and we construct a class of such codes with lengths greater than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q\nu/3</tex> .
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