Finite Fields, with Applications to Combinatorics

Finite Fields: A Gateway to Combinatorial Applications

This book uses finite field theory as a launchpad to introduce a range of ideas from algebra and number theory. It meticulously constructs all finite fields from the ground up and demonstrates their uniqueness up to isomorphism.

As a compelling reward, it presents several combinatorial applications of finite fields, including:

• Sidon sets and perfect difference sets
• de Bruijn sequences and a magic t…