Handbook of finite fields. (©2013)

• Record Type: Book
• Further Information: Note: [edited by] Gary L. Mullen, Daniel Panario.
• Editors: Mullen, Gary L; Panario, Daniel, 1959-
• Contents: 1. History of Finite Fields / Roderick Gow -- Finite fields in the 18th and 19th centuries -- 2. Introduction to Finite Fields -- Basic properties of finite fields / Gary L. Mullen and Daniel Panario -- Tables / David Thomson -- Theoretical Properties -- 3. Irreducible Polynomials -- Counting irreducible polynomials / Joseph L. Yucas -- Construction of irreducible / Melsik Kyuregyan -- Conditions for reducible polynomials / Daniel Panario -- Weights of irreducible polynomials / Omran Ahmadi -- Prescribed coefficients / Stephen D. Cohen -- Multivariate polynomials / Xiang-dong Hou -- 4. Primitive Polynomials -- Introduction to primitive polynomials / Gary L. Mullen and Daniel Panario -- Prescribed coefficients / Stephen D. Cohen -- Weights of primitive polynomials / Stephen D. Cohen -- Elements of high order / José Felipe Voloch -- 5. Bases -- Duality theory of bases / Dieter Jungnickel -- Normal bases / Shuhong Gao and Qunying Liao -- Complexity of normal bases / Shuhong Gao and David Thomson -- Completely normal bases / Dirk Hachenberger -- 6. Exponential and Character Sums -- Gauss, Jacobi, and Kloosterman sums / Ronald J. Evans -- More general exponential and character sums / Antonio Rojas-León -- Some applications of character sums / Alina Ostafe and Arne Winterhof -- Sum-product theorems and applications / Moubariz Z. Garaev -- 7. Equations over Finite Fields -- General forms / Daqing Wan -- Quadratic forms / Robert Fitzgerald -- Diagonal equations / Francis Castro and Ivelisse Rubio -- 8. Permutation Polynomials -- One variable / Gary L. Mullen and Qiang Wang -- Several variables / Rudolf Lidl and Gary L. Mullen -- Value sets of polynomials / Gary L. Mullen and Michael E. Zieve -- Exceptional polynomials / Michael E. Zieve -- 9. Special Functions over Finite Fields -- Boolean functions / Claude Carlet -- PN and APN functions / Pascale Charpin -- Bent and related functions / Alexander Kholosha and Alexander Pott -- k-polynomials and related algebraic objects / Robert Coulter -- Planar functions and commutative semifields / Robert Coulter -- Dickson polynomials / Qiang Wang and Joseph L. Yucas -- Schur's conjecture and exceptional covers / Michael D. Fried. 10. Sequences over Finite Fields -- Finite field transforms / Gary McGuire -- LFSR sequences and maximal period sequences / Harald Niederreiter -- Correlation and autocorrelation of sequences / Tor Helleseth -- Linear complexity of sequences and multisequences / Wilfried Meidl and Arne Winterhof -- Algebraic dynamical systems over finite fields / Igor Shparlinski -- 11. Algorithms -- Computational techniques / Christophe Doche -- Univariate polynomial counting and algorithms / Daniel Panario -- Algorithms for irreducibility testing and for constructing irreducible polynomials / Mark Giesbrecht -- Factorization of univariate polynomials / Joachim von zur Gathen -- Factorization of multivariate polynomials / Erich Kaltofen and Grégoire Lecerf -- Discrete logarithms over finite fields / Andrew Odlyzko -- Standard models for finite fields / Bart de Smit and Hendrik Lenstra -- 12. Curves over Finite Fields -- Introduction to function fields and curves / Arnaldo Garcia and Henning Stichtenoth -- Elliptic curves / Joseph Silverman -- Addition formulas for elliptic curves / Daniel J. Bernstein and Tanja Lange -- Hyperelliptic curves / Michael John Jacobson, Jr. and Renate Scheidler -- Rational points on curves, Arnaldo Garcia and Henning Stichtenoth Towers / Arnaldo Garcia and Henning Stichtenoth -- Zeta functions and L-functions / Lei Fu -- p-adic estimates of zeta functions and L-functions / Régis Blache -- Computing the number of rational points and zeta functions / Daqing Wan -- 13. Miscellaneous Theoretical Topics -- Relations between integers and polynomials over finite fields / Gove Effinger -- Matrices over finite fields / Dieter Jungnickel -- Classical groups over finite fields / Zhe-Xian Wan -- Computational linear algebra over finite fields / Jean-Guillaume Dumas and Clément Pernet -- Carlitz and Drinfeld modules / David Goss -- Applications -- 14. Combinatorial -- Latin squares / Gary L. Mullen -- Lacunary polynomials over finite fields / Simeon Ball and Aart Blokhuis -- Affine and projective planes / Gary Ebert and Leo Storme -- Projective spaces / James W.P. Hirschfeld and Joseph A. Thas -- Block designs / Charles J. Colbourn and Jeffrey H. Dinitz -- Difference sets / Alexander Pott -- Other combinatorial structures / Jeffrey H. Dinitz and Charles J. Colbourn -- (t, m, s)-nets and (t, s)-sequences / Harald Niederreiter -- Applications and weights of multiples of primitive and other polynomials / Brett Stevens -- Ramanujan and expander graphs / M. Ram Murty and Sebastian M. Cioaba. 15. Algebraic Coding Theory -- Basic coding properties and bounds / Ian Blake and W. Cary Huffman -- Algebraic-geometry codes / Harald Niederreiter -- LDPC and Gallager codes over finite fields / Ian Blake and W. Cary Huffman -- Turbo codes over finite fields / Oscar Takeshita -- Raptor codes / Ian Blake and W. Cary Huffman -- Polar codes / Simon Litsyn -- 16. Cryptography -- Introduction to cryptography / Alfred Menezes -- Stream and block ciphers / Guang Gong and Kishan Chand Gupta -- Multivariate cryptographic systems / Jintai Ding -- Elliptic curve cryptographic systems / Andreas Enge -- Hyperelliptic curve cryptographic systems / Nicolas Thériault -- Cryptosystems arising from Abelian varieties / Kumar Murty -- Binary extension field arithmetic for hardware implementations / M. Anwarul Hasan and Haining Fan -- 17. Miscellaneous Applications -- Finite fields in biology / Franziska Hinkelmann and Reinhard Laubenbacher -- Finite fields in quantum information theory / Martin Roetteler and Arne Winterhof -- Finite fields in engineering / Jonathan Jedwab and Kai-Uwe Schmidt.
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2013
• Copyright Date: 2013
• Extent: 1 online resource (xxxv, 1033 pages), illustrations
• Subjects: 512/.3; Finite fields (Algebra); Finite fields (Algebra); COMPUTERS -- Security -- Cryptography; MATHEMATICS -- Number Theory; MATHEMATICS -- Combinatorics; MATHEMATICS -- Algebra -- Intermediate; Finite fields (Algebra); Finite fields (Algebra); Electronic books
• Languages: English
• ISBNs: 9781439873823; 1439873828; 9781299703629; 1299703623
• Related ISBNs: 9781439873786; 143987378X
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.