Entropy function for a q-ary alphabet
= Entropy function for a q-ary alphabet
{title2=$H_q(x)=x\log_q(q-1)-x\log_qx-(1-x)\log_q(1-x)$}
= q-ary entropy
{c}
{synonym}
This is the entropy in base $q$ of the distribution with one symbol of probability $1-x$ and each of the other $q-1$ symbols of probability $x/(q-1)$. It increases on $[0,1-1/q]$ from zero to one, and governs the exponential volume of a <Hamming ball>. For $q=2$ it is the <binary entropy> function.
// Target: algebra.bigb