In coding theory, there exist linear codes, whose code words are generated using a generator matrix. This encoding is done by multiplying the input vector s (aka. information word) from the right with the generator matrix G to obtain the code word w:
w = sG
(see wikipedia > linear codes > hamming codes for an example of a generator matrix)
The above equation defines a linear mapping, but the multiplication of the matrix G from the right is non-standard for linear mappings. The standard is to multiply the matrix from the left, as in
y = Ax ,
where x is the input vector, A is the transformation matrix, and y is the result or output vector.
Why is a generator matrix multiplied from the right instead of from the left?
