Go through all of the necessary steps to build a generator polynomial for a 3-error correcting 11-ary Reed-Solomon code of length $10$.
How to go about this? Based on the formula, $(x−βl+j)$, what could I make $β$? Since it has to be a root of an irreducible polynomial, but I am confused on how to incorporate all this information in this problem. Please help in how to start this problem?
You can actually use an easy formula mentioned earlier in the Spence text (which I assume you're using). Namely, $g(x) = (x - \alpha^b)(x-\alpha^{b+1})...(x-\alpha^{b + \delta - 2})$, where $\delta$ is the desired Hamming distance (in this case, it's $2 * 3 + 1 = 7$), $b$ is any integer $\geq 0$ ($0$ seems like a good choice), and $\alpha$ is a primitive root modulo $11$; for example, $2$.