Generator matrix for linear block code

Question

I have a matrix given and I should check, if it is a valid generator matrix for a linear block code. If not, I should delete all rows needed to get a valid generator matrix. I found one line which results from the sum of two other lines (so it is not linear independent) => I deleted this line. Are there any other things to consider? Someone told me, that the lines also have to be orthogonal but I found a generator matrix for a hamming code (https://wikimedia.org/api/rest_v1/media/math/render/svg/c7074a665f86a45ca5984094b7ecf313b6d371fb) where e.g. line 1 and 3 are not orthogonal.

Answer 1

The rows of the generator matrix must conform a basis. Hence, the only requisite is that they are linearly independent. Orthogonality is not required.