Linear Codes and Syndrome tables Watch
If so only c1 is linear. c1 and c2 have minimum distance 1 because the generator matrix has a column of 1's and c3 has minimum distance 4 because the 4 columns in the vector can add up to give the zero vector.
For c4,c5,c6 I don't see why the minimum distance would be any different and dimension would be 1 for c4 and c5 and c6 because they all have one free variable?
For 2a) I didn't understand what the significance of 'an error-vectore1 = (1, 0, 0, 0, 0) occurs in the channel' i know how to make a syndrome table but I don't know what this is for.