I’m confused as to how to approach the following problem:
Let $C$ be a $7$-ary linear code with generator matrix $$ \left[ \begin{matrix} 0 & 1 & 5 & 5 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 6 & 3 & 2 & 1 \end{matrix} \right]$$ What are the cosets of $C$?
I don’t really understand how to obtain the cosets of the code, though I understand what cosets are in general. What am I missing?