Practice Finite Fields And Properties Ii (1) - Overview 41 - Discrete Mathematics

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6 sample questions

Question 1.
What does the order of a finite field indicate?
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Think about the definition we explored in our discussions.
Question 2.
Define an irreducible polynomial.
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Consider the properties of polynomial expressions.
3Question 3.
What does the order of a finite field represent?
- The total number of elements in the field
- The maximum degree of polynomials
- The characteristic of the field
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Think back to the definition we studied.
4Question 4.
True or False: The characteristic of a finite field is always a composite number.
- True
- False
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Recall our definition of characteristic.
Question 5.
Prove that for any finite field F with characteristic p, the order is of the form p^r for some integer r > 0.
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Investigate how the mapping and linear combinations play a role.
Question 6.
Construct the finite field of order 16 using an irreducible polynomial and verify the properties hold.
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Check the polynomial functions to ensure they adhere to defined field properties.

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