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I have been trying to understand Hamming Codes and wrote a program that correctly encodes and decodes given inputs for Hamming 7,4. When trying to do this for 15,11 I cannot get the right output when trying to encode.

I inputted the byte and added three leading zeros then multiplied it by the generator matrix below. After taking mod2 of the matrix I still am not getting the correct answer and am not sure if I am doing something wrong or if my matrix is incorrect.

int [][] byte = {{0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1}};

int [][] matrixG = { { 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                     { 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
                     { 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0},
                     { 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, 
                     { 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0},
                     { 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0},
                     { 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0},
                     { 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0},
                     { 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0},
                     { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0},
                     { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1} };

Hamming codes are a very new concept to me so I may be missing something very obvious! I really appreciate any help you can give me!

gcrysler
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  • The generator polynomial for Hamming(15,11) is `x^4 + x + 1`, which corresponds to `1 0 0 1 1` cyclic code, instead of `1 1 0 0 1` in your matrix – sw0rdf1sh Sep 29 '19 at 11:50

1 Answers1

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Your G matrix is wrong.

int [][] matrixG = { { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
                     { 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0},
                     { 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
                     { 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
                     { 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1},
                     { 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1},
                     { 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1},
                     { 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1},
                     { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1},
                     { 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1},
                     { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1} };

As you can see here, the G Matrix keeps the original data bits untouched, and appends additional parity bits to the end of your string.

Mat
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