Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 11G / a / Solution

Delete any $d-1$ coordinates. The resulting puncturing mapis injective: if $\pi (x)=\pi (y)$ for distinct codewords, then the nonzero codeword $x-y$ is supported on at most $d-1$ coordinates, contradicting the minimum distance. Thuswhich is the Singleton bound