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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!

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    $\begingroup$ 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 what you would get when using a prescribed generator matrix. $\endgroup$
    – Jyrki Lahtonen
    Commented Jun 17, 2019 at 9:31
  • $\begingroup$ @JyrkiLahtonen Does this mean that i need to code this segment part by part, in such way that i first take first four bit and code them, then bits from 5th to 8th and so on... Is that right? $\endgroup$
    – cdummie
    Commented Jun 17, 2019 at 10:40
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    $\begingroup$ Yes. That's correct. $\endgroup$
    – Jyrki Lahtonen
    Commented Jun 17, 2019 at 10:46
  • $\begingroup$ @JyrkiLahtonen Thanks for help! I appreciate it. $\endgroup$
    – cdummie
    Commented Jun 17, 2019 at 12:34

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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."

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