Handbook of Finite Fields Discrete Mathematics and Its Applications Series
Auteurs : Mullen Gary L., Panario Daniel
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and each chapter is self contained and peer reviewed.
The first part of the book traces the history of finite fields through the eighteenth and nineteenth centuries. The second part presents theoretical properties of finite fields, covering polynomials, special functions, sequences, algorithms, curves, and related computational aspects. The final part describes various mathematical and practical applications of finite fields in combinatorics, algebraic coding theory, cryptographic systems, biology, quantum information theory, engineering, and other areas. The book provides a comprehensive index and easy access to over 3,000 references, enabling you to quickly locate up-to-date facts and results regarding finite fields.
INTRODUCTION: History of Finite Fields. Introduction to Finite Fields. THEORETICAL PROPERTIES: Irreducible Polynomials. Primitive Polynomials. Bases. Exponential and Character Sums. Equations over Finite Fields. Permutation Polynomials. Special Functions over Finite Fields. Sequences over Finite Fields. Algorithms. Curves over Finite Fields. Miscellaneous Theoretical Topics. APPLICATIONS: Combinatorial. Algebraic Coding Theory. Cryptography. Miscellaneous Applications. Bibliography. Index.
Gary L. Mullen is a professor of mathematics at The Pennsylvania State University.
Daniel Panario is a professor of mathematics at Carleton University.
Date de parution : 07-2013
17.8x25.4 cm
Thèmes de Handbook of Finite Fields :
Mots-clés :
Finite Fields; Irreducible Polynomial; theory and applications of finite fields; Minimal Polynomial; history of finite fields; Primitive Polynomials; theoretical properties of finite fields; Permutation Polynomials; finite fields in combinatorics; Dickson Polynomials; finite fields in algebraic coding theory; Irreducible Monic Polynomials; finite fields in cryptographic systems; Newton Polygon; finite fields in quantum information theory; Hyperelliptic Curve; finite fields in biology; Elliptic Curve; finite fields in engineering; Stream Ciphers; tables of polynomials; Abelian Varieties; Discrete Logarithm; Discrete Logarithm Problem; Cayley Graph; Elliptic Curves; MDS Code; Cyclic Code; Character Sums; LFSR; Reed Muller Codes; Galois Extension; Finite Field Fq; Exponential Sums; Reciprocal Roots