How do you find the coset leaders without writing a standard array?

Question

My book seems to produce the coset leaders purely by looking at the generator matrix, but it doesn't say how. I understand that for a q-ary [n,k,d] code there are $q^{n-k}$ coset leaders, but not how to do it without at least writing all the linear combinations of the rows of the generator matrix.

Answer 1

In $[n, k, d]_q$ code has $q^k$ codewords. And in $F_q^n$ has $q^n$ codewords. Every coset has a (only one) coset leader. Number of cosets are $q^n/q^k$. So Number of coset leaders are $q^{n-k}$. A coset leader is a list weighted codeword of the coset. Hope it will work.

What is the name of the book?