[Math] Finding the parity check matrix for (10,6,3) shortened Hamming Code

coding-theorylinear algebra

I am dealing with error correction using a (10,6,3) shortened hamming code. I can do the linear algebra for decoding a (7,4) hamming code so i sort of understand what going on here. However now I am working on a (10,6,3) shortened hamming code and I have not been given the the parity check matrix. i need to implement the decoder in c++.

Best Answer

The answer is too easy.
(1) let G be the generator matrix. Take the identity matrix out of G (2) let P be the remaining n x (n-m) matrix. transpose P (3) add n-m columns to the transpose of P and insert an identity matrix

The result from step 3 will be the H for G.

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