In the book "Fundamentals of Error-Correcting Codes" this was written
One way to find the generating idempotent $e(x)$ for a cyclic code $C$ from the generator polynomial $g(x)$ is to solve $1 = a(x)g(x) + b(x)h(x)$ for $a(x)$ using the Euclidean Algorithm, where $h(x) = (x^n − 1)/g(x)$. Then reducing $a(x)g(x)$ modulo $x^n − 1$ produces $e(x)$. could any one help me How this
For example I cant verify this when i try to solve : Exercise 218 : Verify the entries in the table in Example 4.3.4. page(133) the book thanks