Practice Mapping from ℤ^r to Field F - 1.6 | Overview 41 | Discrete Mathematics - Vol 3
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Mapping from ℤ^r to Field F

1.6 - Mapping from ℤ^r to Field F

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the order of a finite field?

💡 Hint: Think about the prime number's role in determining the number of elements.

Question 2 Easy

Define a minimal spanning set.

💡 Hint: Consider redundancy in spanning the field.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the order of a finite field?

p^r
r^p
pq
None of the above

💡 Hint: Focus on the relationship between the prime and the number of elements.

Question 2

True or False: Every polynomial can be used to construct a finite field.

True
False

💡 Hint: Consider the properties needed for a polynomial to work for fields.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Construct a finite field of order 16 and describe the process involved in selecting the irreducible polynomial.

💡 Hint: Keep in mind the necessary properties of irreducible polynomials.

Challenge 2 Hard

Demonstrate that for any finite field with order p^r, the mapping function g is bijective.

💡 Hint: Refer back to the properties of linear combinations and minimal spanning sets.

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