The degree of a monomial is defined as the sum of exponents of all the variables.
To evaluate a monomial at some position, we just replace all the variables with the corresponding values to do computation. The only caveat in our case is that computations are done modulo 2.
Procedure:
Step 1: Enter the degree of monomial \(M(\textbf{X})\) and click "Check" to verify your answer. If your answer is correct you will move on to the next section.
Step 2: For the same monomial, evaluate it all values in \(\mathbb{F}_2^3\). We assume the variables are indexed as \((X_1, X_2, X_3)\).
What is the degree of the message monomial?
Reed-Muller Code Evaluation
Find the codeword in the \(3^{\text{rd}}\) order Reed-Muller code corresponding to this given monomial.
Do this by entering the evaluations at tuples \((X_{1}, X_{2}, X_{3}) \in \{0,1\}^3\) which are indicated over the text-boxes shown.