Finite Fields: Theory, Fundamental Properties and Applications

Janet Simmons (Editor)

Series: Mathematics Research Developments
BISAC: MAT009000

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This book provides new research in finite fields. Chapter One presents some techniques that rely on a combination of results from graph theory, finite fields, matrix theory, and finite geometry to researchers working in the area of preserver problems. It also gives a brief presentation of this research field to other mathematicians. Chapter Two contains a basic and self-contained introduction to classical coherent state transforms, namely classical wavelet and classical wave-packet transforms, on finite fields. Chapter Three proposes an intrinsic representation of finite mƟ extension as this is a tradition for finite extension fields. Chapter Four reviews mƟ cyclic codes on a mƟ field. Chapter Five discusses recent results concerning the number of solutions to certain equations in several variables over finite fields. (Imprint: Nova)

Preface

Chapter 1. Preserver Problems Over Finite Fields
Marko Orel (Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Koper, Slovenia, and others)

Chapter 2. Classical Coherent State Transforms over Finite Fields
Arash Ghaani Farashahi (Numerical Harmonic Analysis Group (NuHAG), Faculty Mathematics, University of Vienna, Vienna, Austria)

Chapter 3. The Structure of Finite mƟ Field Intrinsic Anatomy
Fidèle Ayissi Etémé (The University of Yaounde, Higher Teacher's Training College, Department of Mathematics, Yaounde, Cameroon)

Chapter 4. mƟ Cyclic Codes on a mƟ Field
Fidèle Ayissi Etémé and Jean Armand Tsimiy (The University of Yaounde, Higher Teacher's Training College, Department of Mathematics, Yaounde, Cameroon, and others)

Chapter 5. On Two Problems of Carlitz and their Generalizations
Ioulia N. Baoulina (Department of Mathematics, Moscow State Pedagogical University, Moscow, Russia)

Index

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