Practice Construction of Finite Field with 9 Elements - 22.1 | 22. Finite Fields and Properties I | Discrete Mathematics - Vol 3
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Construction of Finite Field with 9 Elements

22.1 - Construction of Finite Field with 9 Elements

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define finite field and give an example.

💡 Hint: Think about the number of elements in the field.

Question 2 Easy

What is an irreducible polynomial?

💡 Hint: Consider how polynomials behave similar to numbers.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

💡 Hint: Think about what happens if you keep adding 1.

Question 2

Is the characteristic of a finite field always a prime number?

True
False

💡 Hint: Consider the implications of composite numbers.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Construct the polynomial multiplication table for the elements of F and determine the product of (x + 1)(x + 2).

💡 Hint: Remember to reduce after multiplication and apply the modulo.

Challenge 2 Hard

Using F, show that multiplying each polynomial by the element 2 generates a cyclic group. List the non-zero elements produced.

💡 Hint: Keep track of each step, reducing properly along the way.

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