MATH: Simple Linear Codes/Algebra Question
 

I'm surprised to see the lack of math questions in this forum, so I'll be cross-posting in the Probability forum to hopefully get an answer.

Suppose v_1 is one of the code words in the basis for C where q=2, n=4, and M = 4

v_1 = (0 0 1 1)

What is 2*(0 0 1 1)?
(This will solve why I get c_1*v_1 + c_2*v_2 + c_3*v_3 = 0 for c_1 = c_2 = c_3 = 2, which is incorrect)