Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 1 / 11I / b / iv

Put $q=2d-n>0$. If $M$ is even, part (iii) givessoBecause $M$ is even,

If $M$ is odd, part (iii) instead givesCancelling $M-1$ yields $qM\le n=2d-q$, and thereforeSince $M$ is an integer, the same desired upper bound follows. Thus the binary Plotkin bound is