I am supposed to find the generator matrix of a polynomial generator $g(x)=1+x+x^3+x^4\cdots$ with given $(n,k)$, $n=7$ but $k$ is not specified...
how many shifts should I go to get a systematic form?
how do I find the generator matrix of binary cyclic codes with given number of column but not rows?
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polynomials
coding-theory
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1The codewords are the coefficient of polynomials of $<7$ which are divisible by $g(x)$. So, from this, you see specifying $n$, $g(x)$ gives you $k$. – 2017-01-01
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0So how do I go on to find the generator matrix? – 2017-01-01
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0Found the answer if someone is interested. – 2017-01-02