On the maximum of the weighted binomial sum $2^{-r}{\sum }_{i=0}^r\left(\genfrac{}{}{0ex}{}{m}{i}\right)$

S. P. Glasby, G. R. Paseman

The weighted binomial sum $f_m(r)=2^{-r}{\sum }_{i=0}^r\left(\genfrac{}{}{0ex}{}{m}{i}\right)$ arises in coding theory and information theory. We prove that,for $m\notin \{0,3,6,9,12\}$, the maximum value of…