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Reed-Muller Codes - Polynomial View of Encoding

1. Let f(X)=X2+X+1f(X) = X^2 + X + 1 be a polynomial over F2\mathbb{F}_2. What is the value of f(1) modulo 2?

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2. Let f(X)=X3+X2+1f(X) = X^3 + X^2 + 1 be a polynomial over F2\mathbb{F}_2. What is the value of f(0)?

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3. What is the sum of the polynomials f(X)=X2+Xf(X) = X^2 + X and g(X)=X2+1g(X) = X^2 + 1 in F2[X]\mathbb{F}_2[X]?
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4. What is the degree of the polynomial f(X)=(X3+X2+1)+(X3+X+1)f(X) = (X^3 + X^2 + 1) + (X^3 + X + 1)?

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5. Which of the following is a root of the polynomial f(X)=X2+1f(X) = X^2 + 1 in F2\mathbb{F}_2?

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