Solution
= Solution
The parity-check <matrix> has rank $3$, so its kernel has dimension $7-3=4$ and size $16$; see <linear code>. Its columns are precisely the seven distinct nonzero <vectors> of $\mathbb F_2^3$. Thus no weight-one or weight-two word is in the kernel, while three dependent columns give a weight-three word. Hence $d=3$.