Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 3K / c / Solution

Yes, for a binary code. Correcting $e$ errors requires minimum distance at least $2e+1$. Apply the parity extension: append to each word the bit that makes its total weight even. Every odd distance increases by one and every even distance is unchanged, so the extended minimum distance is at least $2e+2$. It therefore detects every pattern of at most $2e+1$ errors.