Hi,
I am a newbie working in polynomial quotient rings:
I want to implement the Patterson algorithm to decode Goppa Codes.
Therefore, I need to split a polynomial p in a quotient ring in its
even part p0 and its odd part p1
such that p(z) = p0^2(z)+z*p1^2(z). I run into several problems to do
so in SAGE:

m = 4
F.<x> = PolynomialRing(GF(2))
xx = F.gen()
S.<x> = F.quotient(x^m + x + 1)
print S
u = S.gen()
N = 2^m-1
n = 8
F_E.<X> = PolynomialRing(S)
g = X

split(g)? how?

help please

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