Solution
= Solution
The Mariner code is $\operatorname{RM}(5,1)$ with parameters $[32,6,16]$. Its information rate is $6/32=3/16$, and it corrects
$$
\left\lfloor\frac{16-1}{2}\right\rfloor=7
$$
errors, 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 $1/31$.