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

The Mariner code is $\mathrm{RM}(5,1)$ with parameters $[32,6,16]$. Its information rate is $6/32=3/16$, and it correctserrors, a proportion $7/32$ of a codeword. The binary Hamming code of length $31$ has parameters $[31,26,3]$: its rate $26/31$ is much higher, but it corrects only one error, a proportion $1/31$.