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 NPTEL >> Courses >> Electronics & Communication Engineering >> Coding Theory (Video) >> Introduction to Linear Block Codes
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 Question: Dear Sir, How we arrive at this G.Also in literature this matrix only appears as example. My doubt is actually the first 3 col.s how we choose XORing G = [1 1 0 1 0 0 0; 0 1 1 0 1 0 0; 1 1 1 0 0 1 0; 1 0 1 0 0 0 1]; There are other possibilities to get good code , isn' By: Devanand T     Date: 2012-11-02 Answer: Yes, there are several other codes with n=7 and k=4, like the one given here. G = [1 1 0 1 0 0 0; 0 1 1 0 1 0 0; 1 1 1 0 0 1 0; 1 0 1 0 0 0 1]; The above happens to be a generator matrix for the (7,4,3) Hamming code, which is a very famous code historically. It is also a useful code in practice for small lengths. Also, if you want a linear code with n=7, k=4 and d=3, you will not get anything very different from the Hamming code. For the above reasons, it is given as an example in many texts. You could definitely work with other examples, particularly for other values of n and k and d. By: Dr. Andrew Thangaraj     Date: 2012-11-06
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