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ORCIDHandbook of Finite Fields, 2013
- Gary L. Mullen, Daniel Panario:
Handbook of Finite Fields. Discrete mathematics and its applications, CRC Press 2013, ISBN 978-1-439-87378-6
Introduction
- Roderick Gow:
History of finite fields : Finite fields in the 18-th and 19-th centuries. Handbook of Finite Fields 2013: 3-12 - Gary L. Mullen, Daniel Panario:
Introduction to finite fields : Basic properties of finite fields. Handbook of Finite Fields 2013: 13-31 - David Thomson:
Tables. Handbook of Finite Fields 2013: 32-52
Theoretical Properties. Irreducible Polynomials
- Joseph L. Yucas:
Counting irreducible polynomials. Handbook of Finite Fields 2013: 53-59 - Melsik K. Kyuregyan:
Construction of irreducible. Handbook of Finite Fields 2013: 60-65 - Daniel Panario:
Conditions for reducible polynomials. Handbook of Finite Fields 2013: 66-69 - Omran Ahmadi:
Weights of irreducible polynomials. Handbook of Finite Fields 2013: 70-72 - Stephen D. Cohen:
Prescribed coefficients. Handbook of Finite Fields 2013: 73-78 - Xiang-dong Hou:
Multivariate polynomials. Handbook of Finite Fields 2013: 79-86
Primitive Polynomials
- Gary L. Mullen, Daniel Panario:
Introduction to primitive polynomials. Handbook of Finite Fields 2013: 87-89 - Stephen D. Cohen:
Prescribed coefficients. Handbook of Finite Fields 2013: 90-94 - Stephen D. Cohen:
Weights of primitive polynomials. Handbook of Finite Fields 2013: 95-97 - José Felipe Voloch:
Elements of high order. Handbook of Finite Fields 2013: 98-100
Bases
- Dieter Jungnickel:
Duality theory of bases. Handbook of Finite Fields 2013: 101-108 - Shuhong Gao, Qunying Liao:
Normal bases. Handbook of Finite Fields 2013: 109-116 - Shuhong Gao, David Thomson:
Complexity of normal bases. Handbook of Finite Fields 2013: 117-127 - Dirk Hachenberger:
Completely normal bases. Handbook of Finite Fields 2013: 128-138
Exponential and Character Sums
- Ronald J. Evans:
Gauss, Jacobi, and Kloosterman sums. Handbook of Finite Fields 2013: 139-160 - Antonio Rojas-León:
More general exponential and character sums. Handbook of Finite Fields 2013: 161-169 - Alina Ostafe, Arne Winterhof:
Some applications of character sums. Handbook of Finite Fields 2013: 170-184 - Moubariz Z. Garaev:
Sum-product theorems and applications. Handbook of Finite Fields 2013: 185-192
Equations over Finite Fields
- Daqing Wan:
General forms. Handbook of Finite Fields 2013: 193-200 - Robert Fitzgerald:
Quadratic forms. Handbook of Finite Fields 2013: 201-205 - Francis N. Castro, Ivelisse Rubio:
Diagonal equations. Handbook of Finite Fields 2013: 206-214
Permutation Polynomials
- Gary L. Mullen, Qiang Wang:
One variable. Handbook of Finite Fields 2013: 215-229 - Rudolf Lidl, Gary L. Mullen:
Several variables. Handbook of Finite Fields 2013: 230-231 - Gary L. Mullen, Michael E. Zieve:
Value sets of polynomials. Handbook of Finite Fields 2013: 232-235 - Michael E. Zieve:
Exceptional polynomials. Handbook of Finite Fields 2013: 236-240
Special Functions over Finite Fields
- Claude Carlet:
Boolean functions. Handbook of Finite Fields 2013: 241-252 - Pascale Charpin:
PN and APN functions. Handbook of Finite Fields 2013: 253-261 - Alexander Kholosha, Alexander Pott:
Bent and related functions. Handbook of Finite Fields 2013: 262-272 - Robert S. Coulter:
k-polynomials and related algebraic objects. Handbook of Finite Fields 2013: 273-277 - Robert S. Coulter:
Planar functions and commutative semifields. Handbook of Finite Fields 2013: 278-281 - Qiang Wang, Joseph L. Yucas:
Dickson polynomials. Handbook of Finite Fields 2013: 282-289 - Michael D. Fried:
Schur?s conjecture and exceptional covers. Handbook of Finite Fields 2013: 290-302
Sequences over Finite Fields
- Gary McGuire:
Finite field transforms. Handbook of Finite Fields 2013: 303-310 - Harald Niederreiter:
LFSR sequences and maximal period sequences. Handbook of Finite Fields 2013: 311-316 - Tor Helleseth:
Correlation and autocorrelation of sequences. Handbook of Finite Fields 2013: 317-323 - Wilfried Meidl, Arne Winterhof:
Linear complexity of sequences and multisequences. Handbook of Finite Fields 2013: 324-336 - Igor E. Shparlinski:
Algebraic dynamical systems over finite fields. Handbook of Finite Fields 2013: 337-344
Algorithms
- Christophe Doche:
Computational techniques. Handbook of Finite Fields 2013: 345-363 - Daniel Panario:
Univariate polynomial counting and algorithms. Handbook of Finite Fields 2013: 364-373 - Mark Giesbrecht:
Algorithms for irreducibility testing and for constructing irreducible polynomials. Handbook of Finite Fields 2013: 374-379 - Joachim von zur Gathen:
Factorization of univariate polynomials. Handbook of Finite Fields 2013: 380-381 - Erich L. Kaltofen, Grégoire Lecerf:
Factorization of multivariate polynomials. Handbook of Finite Fields 2013: 382-392 - Andrew M. Odlyzko:
Discrete logarithms over finite fields. Handbook of Finite Fields 2013: 393-400 - Bart de Smit, Hendrik Lenstra:
Standard models for finite fields. Handbook of Finite Fields 2013: 401-404
Curves over Finite Fields
- Arnaldo Garcia, Henning Stichtenoth:
Introduction to function fields and curves. Handbook of Finite Fields 2013: 405-421 - Joseph H. Silverman:
Elliptic curves. Handbook of Finite Fields 2013: 422-439 - Daniel J. Bernstein, Tanja Lange:
Addition formulas for elliptic curves. Handbook of Finite Fields 2013: 440-446 - Michael J. Jacobson Jr., Renate Scheidler:
Hyperelliptic curves. Handbook of Finite Fields 2013: 447-455 - Arnaldo Garcia, Henning Stichtenoth:
Rational points on curves. Handbook of Finite Fields 2013: 456-463 - Arnaldo Garcia, Henning Stichtenoth:
Towers. Handbook of Finite Fields 2013: 464-468 - Lei Fu:
Zeta functions and L-functions. Handbook of Finite Fields 2013: 469-478 - Régis Blache:
p-adic estimates of zeta functions and L-functions. Handbook of Finite Fields 2013: 479-487 - Daqing Wan:
Computing the number of rational points and zeta functions. Handbook of Finite Fields 2013: 488-492
Miscellaneous Theoretical Topics
- Gove Effinger:
Relations between integers and polynomials over finite fields. Handbook of Finite Fields 2013: 493-499 - Dieter Jungnickel:
Matrices over finite fields. Handbook of Finite Fields 2013: 500-509 - Zhe-Xian Wan:
Classical groups over finite fields. Handbook of Finite Fields 2013: 510-519 - Jean-Guillaume Dumas, Clément Pernet:
Computational linear algebra over finite fields. Handbook of Finite Fields 2013: 520-534 - David Goss:
Carlitz and Drinfeld modules. Handbook of Finite Fields 2013: 535-548
Applications. Combinatorial
- Gary L. Mullen:
Latin squares. Handbook of Finite Fields 2013: 550-555 - Simeon Ball, Aart Blokhuis:
Lacunary polynomials over finite fields. Handbook of Finite Fields 2013: 556-562 - Gary L. Ebert, Leo Storme:
Affine and projective planes. Handbook of Finite Fields 2013: 563-573 - James W. P. Hirschfeld, Joseph A. Thas:
Projective spaces. Handbook of Finite Fields 2013: 574-588 - Charles J. Colbourn, Jeffrey H. Dinitz:
Block designs. Handbook of Finite Fields 2013: 589-598 - Alexander Pott:
Difference sets. Handbook of Finite Fields 2013: 599-606 - Jeffrey H. Dinitz, Charles J. Colbourn:
Other combinatorial structures. Handbook of Finite Fields 2013: 607-618 - Harald Niederreiter:
(t, m, s)-nets and (t, s)-sequences. Handbook of Finite Fields 2013: 619-629 - Brett Stevens:
Applications and weights of multiples of primitive and other polynomials. Handbook of Finite Fields 2013: 630-641 - M. Ram Murty, Sebastian M. Cioaba:
Ramanujan and expander graphs. Handbook of Finite Fields 2013: 642-658
Algebraic Coding Theory
- Ian F. Blake, W. Cary Huffman:
Basic coding properties and bounds. Handbook of Finite Fields 2013: 659-702 - Harald Niederreiter:
Algebraic-geometry codes. Handbook of Finite Fields 2013: 703-712 - Ian F. Blake, W. Cary Huffman:
LDPC and Gallager codes over finite fields. Handbook of Finite Fields 2013: 713-726 - Oscar Y. Takeshita:
Turbo codes over finite fields. Handbook of Finite Fields 2013: 727-734 - Ian F. Blake, W. Cary Huffman:
Raptor codes. Handbook of Finite Fields 2013: 727-740 - Simon Litsyn:
Polar codes. Handbook of Finite Fields 2013: 741-740
Cryptography
- Alfred Menezes:
Introduction to cryptography. Handbook of Finite Fields 2013: 741-749 - Guang Gong, Kishan Chand Gupta:
Stream and block ciphers. Handbook of Finite Fields 2013: 750-763 - Jintai Ding:
Multivariate cryptographic systems. Handbook of Finite Fields 2013: 764-783 - Andreas Enge:
Elliptic curve cryptographic systems. Handbook of Finite Fields 2013: 784-796 - Nicolas Thériault:
Hyperelliptic curve cryptographic systems. Handbook of Finite Fields 2013: 797-803 - Kumar Murty:
Cryptosystems arising from Abelian varieties. Handbook of Finite Fields 2013: 803-810 - M. Anwarul Hasan, Haining Fan:
Binary extension field arithmetic for hardware implementations. Handbook of Finite Fields 2013: 811-824
Miscellaneous Applications
- Franziska Hinkelmann, Reinhard C. Laubenbacher:
Finite fields in biology. Handbook of Finite Fields 2013: 825-834 - Martin Roetteler, Arne Winterhof:
Finite fields in quantum information theory. Handbook of Finite Fields 2013: 834-840 - Jonathan Jedwab, Kai-Uwe Schmidt:
Finite fields in engineering. Handbook of Finite Fields 2013: 841-850
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