Let's say we have a matrix
$ H= \begin{bmatrix} 0 & 0 & 0 & 1 & 1 & 1 & 1 \\ 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 \end{bmatrix} $
Which is a hamming code parity check matrix
I need to find code generator matrix and then find code words if sequence being sent is $ 0 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0$
Now, when i find code generator matrix, its dimensions are supposed to be 4x7. Since i have a sequence of twelve numbers. How am i supposed to determine the code words when number of elements in a given sequence is not equal to number of rows of generator matrix so multiplication of that vector and generator matrix is not possible? Any help appreciated!
This question was answered to some satisfaction in the comment by Jyrki Lahtonen, as written by the poster in another comment.
From the comments:
"In block coding, when using an (n,k) block code, the message to be transmitted is split into blocks of k bits. These are then encoded to match that you would get when using a prescribed generator matrix."