Information positions vs. parity check positions

A generator matrix for a code is a kxn matrix such that the linear span of the rows of this matrix is the code. Such a matrix must have rank k, and therefore it is possible (by doing row operations and also column permutations) to put it in the form:

G = [ I | A ]

Where I is a kxk identity matrix and A is a kxn-k matrix. Two codes are equivalent if one can be gotten from the other by permuting coordinates so any code is equivalent to a code having a generator matrix of the form above. Given such a generator matrix we say that the first k coordinates are information positions and the last n-k coordinates are redundancy or parity-check positions. If we trace back the first k coordinates to find where they were before any permutations were applied, we have found a set of information positions for the original code. Many k-subsets of the coordinates of a code may constitute a so-called information set.