Exercise
Which of the following codes in (Z/3Z)3 is a (3,2)-code?
{(-1,0,0), (0,0,0), (1,0,0)}.
The code generated by (1,-1,0), (0,1,1), and (1,0,1).
{(1,0,0), (-1,0,0), (0,1,0), (0,-1,0)}.
This is a
(3,1)-code, because it is generated by (1,0,0).
Indeed, because it has basis
(1,-1,0) and (1,0,1).
This is not even a linear code; for instance, (0,0,0) is missing.