Practice Construction Of Finite Field With 9 Elements (22.1)

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6 sample questions

Question 1.
Define finite field and give an example.
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Think about the number of elements in the field.
Question 2.
What is an irreducible polynomial?
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Consider how polynomials behave similar to numbers.
3Question 3.
What does the characteristic of a finite field represent?
- The number of elements
- The size of the field
- The smallest integer m such that m times 1 = 0
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Think about what happens if you keep adding 1.
4Question 4.
Is the characteristic of a finite field always a prime number?
- True
- False
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Consider the implications of composite numbers.
Question 5.
Construct the polynomial multiplication table for the elements of F and determine the product of (x + 1)(x + 2).
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Remember to reduce after multiplication and apply the modulo.
Question 6.
Using F, show that multiplying each polynomial by the element 2 generates a cyclic group. List the non-zero elements produced.
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Keep track of each step, reducing properly along the way.

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