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Finite fields provide an enabling background for important applications in electrical engineering, computer science, physics, and even biology. While new developments have emerged in recent years, many researchers still use old problem-solving methods that often lead to inaccurate results and solutions. Poised to become the standard in the field, this up-to-date handbook covers all the theoretical aspects of the finite fields. It also presents numerous applications to communications, coding theory, cryptography, elliptic curves, computer science, and physics.