By <parity extension>, each code keeps size $16$, gains length $8$, and has distance $4$. Extension is injective. A common extended word punctures to a word in $H\cap K$, so only the zero and all-one words occur; both extend to $00000000$ and $11111111$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 11H / b / i / Solution

 Solution (source code)