Practice Mapping From ℤ^r To Field F (1.6) - Overview 41 - Discrete Mathematics

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6 sample questions

Question 1.
What is the order of a finite field?
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Think about the prime number's role in determining the number of elements.
Question 2.
Define a minimal spanning set.
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Consider redundancy in spanning the field.
3Question 3.
What is the order of a finite field?
- p^r
- r^p
- pq
- None of the above
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Focus on the relationship between the prime and the number of elements.
4Question 4.
True or False: Every polynomial can be used to construct a finite field.
- True
- False
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Consider the properties needed for a polynomial to work for fields.
Question 5.
Construct a finite field of order 16 and describe the process involved in selecting the irreducible polynomial.
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Keep in mind the necessary properties of irreducible polynomials.
Question 6.
Demonstrate that for any finite field with order p^r, the mapping function g is bijective.
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Refer back to the properties of linear combinations and minimal spanning sets.

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