1. Consider GF(24) defined via the irreducible polynomial f(x)=X+X3+1 (note that this is not the standard...

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1. Consider GF(24) defined via the irreducible polynomial f(x)=X+X3+1 (note that this is not the "standard" degree-4 polynomial). (a) Write a for i = 1,..., 15 as a polynomial in a of degree at most 3. (b) Find the minimal polynomial of a. (c) Find the minimal polynomial of a. (d) Show that GF (22) is actually contained within GF(24). That is, find 4 elements of GF(24) that are related exactly as the 4 elements of GF(22) are. 1. Consider GF(24) defined via the irreducible polynomial f(x)=X+X3+1 (note that this is not the "standard" degree-4 polynomial). (a) Write a for i = 1,..., 15 as a polynomial in a of degree at most 3. (b) Find the minimal polynomial of a. (c) Find the minimal polynomial of a. (d) Show that GF (22) is actually contained within GF(24). That is, find 4 elements of GF(24) that are related exactly as the 4 elements of GF(22) are.