Practice Existence Of Irreducible Polynomials (1.9) - Overview 41 - Discrete Mathematics

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6 sample questions

Question 1.
Define what a finite field is.
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Think about how many elements are included and what letters represent those elements.
Question 2.
What defines an irreducible polynomial?
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Consider its ability to be broken down into simpler polynomials.
3Question 3.
What is the characteristic of a finite field?
- Any integer
- An irrational number
- A prime number
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Consider what properties of numbers define a field's characteristic.
4Question 4.
True or False: Every polynomial can be factored over finite fields.
- True
- False
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Think about polynomials that can and cannot be broken down further.
Question 5.
Prove that the polynomial x^2 + 1 is irreducible over GF(5).
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Evaluate the polynomial at each element of the field.
Question 6.
Construct a field GF(2^3) using an irreducible polynomial.
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Identify coefficients for the polynomial from GF(2) and how they contribute to the field.

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