Hamming ball volume exponent
= Hamming ball volume exponent
{c}
{title2=$\lim_{n\to\infty}n^{-1}\log_qV_q(n,\lfloor\rho n\rfloor)=H_q(\rho)$}
For $0\le\rho\le1-1/q$, the exponential growth rate of a q-ary Hamming ball is $H_q(\rho)$. <Stirling's formula> gives the exponent of each summand $\binom ni(q-1)^i$, and the sum lies between its largest term and $n+1$ times that term. Above the entropy-maximizing radius fraction, the exponent is one.
// Target: algebra.bigb