On the fractional weight of distinct binaryn-tuples (Corresp.)

It is shown that the fraction
p
of ones in the
Mn
positions of
M
distinct binary
n
-tuples satisfies the inequality \begin{equation} h(p) \geq (l/n) \log_2 M \end{equation} where
h(p) = - p log_2 p - (1 - p) log_2 (1 - p)
is the binary entropy function. This inequality, which simplifies the derivation of the distance property of the Justesen codes, is proved using an elegant information-theoretic argument due to Kriz.