A $(7,4)$ cyclic codes has a generator polynomial: $g(X)=X^{3}+X+1$ (b) Find the generator and parity matrices in systematic form.
Explanation
The generator matrix G in systematic form is obtained by dividing the generator polynomial g(X) into three parts: g_1(X), g_2(X), and g_3(X). The parity-check matrix P is obtained by taking the coefficients of g_1(X), g_2(X), and g_3(X) as columns.
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