Question: Math Coding Theory Problem: PROBLEM 1. Find all monic irreducible degree 4 polynomials in Zor]. (Hint: A degree 4 polynomial is determined by 4 numbers

Math Coding Theory Problem:

PROBLEM 1. Find all monic irreducible degree 4 polynomials in Zor]. (Hint: A degree 4 polynomial is determined by 4 numbers a, b, c, d: f(x) = x tar the'ter+d. f(r) must not be divisible by r or r + 1. What conditions does this impose on a, b, c, d? Also, f(x) must not be a product of degree 2 polynomials. There is only one irreducible degree 2 polynomial in Zelx].)

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