C&O 331 Lecture summaries - Week 9
Lecture 25:
(Mar 8)
Introduction to finite fields
Fact: A finite field of order q exists if and only if q is a prime power.
The characteristic of a finite field.
Definition of an irreducible polynomial.
Construction of finite fields of order p^n.
Example of a finite field of order 4.
Examples of finite fields of order 8.
The Galois field of order
q
.
The frosh's dream
Lecture 26:
(Mar 10)
No lecture (midterm test)
Lecture 27:
(Mar 12)
Introduction to finite fields
Fermat's little theorem for finite fields.
Orders of nonzero fields elements
Definition of a generator (primitive element) of a finite field.
Every finite field has a generator.