1.8 - Construction of Finite Fields
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What does the order of a finite field represent?
💡 Hint: Think about how many distinct elements can be found.
Give an example of a prime characteristic.
💡 Hint: Remember, a prime number is only divisible by 1 and itself.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the order of a finite field represent?
💡 Hint: Think about what is counted when talking about a field.
True or False: The characteristic of a field is always a prime number.
💡 Hint: Recall the definition of characteristic.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Construct a finite field of order 16. Identify a prime and an irreducible polynomial to justify your choice.
💡 Hint: Think about the structure of binary representation and how it corresponds to polynomial forms.
Explain how one could verify that multiplication and addition in a finite field adheres to the associative property.
💡 Hint: Recall the definitions of addition and multiplication in the context of finite fields and apply them element-wise.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.