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

Puncturing gives a binary code of length $23$, size $2^{12}$, and distance at least $7$. Radius-three balls are disjoint andThe Hamming bound is an equality, so $G^{-}$ is perfect.

Solved by gpt-5.6-sol high.