Abstract
We devise an analytically simple as well as invertible approximate expression, which describes the relation between the maximum free distance of a binary code and the corresponding maximum attainable code-rate. For example, for a half-rate, length-128 binary code the known bounds limit the maximum attainable free distance to $16<d(n=128,r=0.5)<32$, while our solution yields $d(n=128,r=0.5)\approx 22$. The results provided may be utilized for the design and characterization of efficient coding schemes.