Handbook of Finite Fields

This extensive reference covers the theory and applications of finite fields, making the Handbook of Finite Fields an invaluable resource for researchers and practitioners alike.

The Handbook of Finite Fields serves as a comprehensive reference dedicated to the intricate theory and diverse applications of finite fields. With contributions from over 80 international experts, this handbook compiles cutting-edge research, making it an essential resource for both scholars and practitioners. Edited by two distinguished researchers, the book maintains a consistent style and format throughout, ensuring that each chapter is self-contained and rigorously peer-reviewed.

In the first section, the Handbook of Finite Fields explores the historical development of finite fields, tracing their evolution through the 18th and 19th centuries. This historical context provides a foundation for understanding the subsequent theoretical advancements. The second section delves into the theoretical properties of finite fields, discussing critical topics such as polynomials, sequences, algorithms, and curves, along with their computational implications.

The final part of the book highlights a variety of mathematical and practical applications of finite fields, spanning areas such as combinatorics, algebraic coding theory, cryptography, biology, quantum information theory, and engineering. With a comprehensive index and access to over 3,000 references, the Handbook of Finite Fields allows readers to efficiently find up-to-date information and results regarding finite fields.