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I'm reading Digital Communications, Proakis, and in order to classify an encoder as catastrophic or noncatastrophic I need the GCD of the elements in the generator G(D).

I don't really know what kind of math is being used, but does not seem as simple polynomial gcd to me.

It's not urgent, thanks!

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It is polynomial math but the field is not the real (or complex) number field but rather the binary field GF$(2)$ in which addition and multiplication are done modulo 2. Hence, $$(1+D)^2 = 1 + 2D + D^2 \equiv 1 + D^2 \bmod 2$$ showing that $1+D$ divides $1+D^2$ (modulo 2) and so their greatest common divisor is just $1+D$ as claimed.

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