1  15
 Shparlinski, Igor E.
 Dordrecht ; Boston : Kluwer Academic Publishers, c1999.
 Description
 Book — xiv, 528 p. : ill. ; 25 cm.
 Summary

 Preface. Acknowledgments. Notation. Introduction. Links flowchart. 1. Polynomial Factorization. 2. Finding Irreducible and Primitive Polynomials. 3. The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices. 4. Bases and Computation in Finite Fields. 5. Coding Theory and Algebraic Curves. 6. Elliptic Curves. 7. Recurrence Sequences in Finite Fields and Cyclic Linear Codes. 8. Finite Fields and Discrete Mathematics. 9. Congruences. 10. Some Related Problems.
 Appendix 1.
 Appendix 2.
 Appendix 3. References. Index.
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QA247.3 .S477 1999  Available 
 Shparlinski, Igor E.
 Dordrecht : Springer Netherlands, 1999.
 Description
 Book — 1 online resource (xiv, 528 pages) Digital: text file.PDF.
 Summary

 Preface. Acknowledgments. Notation. Introduction. Links flowchart. 1. Polynomial Factorization. 2. Finding Irreducible and Primitive Polynomials. 3. The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices. 4. Bases and Computation in Finite Fields. 5. Coding Theory and Algebraic Curves. 6. Elliptic Curves. 7. Recurrence Sequences in Finite Fields and Cyclic Linear Codes. 8. Finite Fields and Discrete Mathematics. 9. Congruences. 10. Some Related Problems.
 Appendix 1.
 Appendix 2.
 Appendix 3. References. Index.
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 Shparlinski, Igor E.
 Basel ; Boston : Birkhäuser, c1999.
 Description
 Book — viii, 180 p ; 24 cm.
 Summary

 Part 1 Preliminaries: introduction
 basic notation and definitions
 auxiliary results. Part 2 Approximation and complexity of the discrete logarithm: approximation of the discrete logarithm module p
 approximation of the discrete logarithm module p1
 approximation of the discrete logarithm by Boolean functions
 approximation of the discrete logarithm by real and complex. Part 3 Complexity of breaking the DiffieHellman cryptosystem: polynomial approximation and arithmetic complexity of the diffieHellman key
 Boolean complexity of the DiffieHellman key. Part 4 Other applications: tradeoff between the Boolean and arithmetic depths of module p functions
 special polynomial and Boolean functions
 RSA and Blum generators of pseudorandom numbers. Part 5 Concluding remarks: generalizations and open questions
 further perspectives. Bibliography.
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QA267.7 .S57 1999  Available 
 Shparlinski, Igor E.
 Dordrecht : Springer Netherlands, 1992.
 Description
 Book — 1 online resource (xii, 240 pages) Digital: text file.PDF.
 Summary

 Series Editor's Preface. Preface. Notations. Introduction. 1. Polynomial Factorization. 2. Finding Irreducible and Primitive Polynomials. 3. The Distribution of Irreducible and Primitive Polynomials. 4. Bases and Computation in Finite Fields. 5. Coding Theory and Algebraic Curves. 6. Elliptic Curves. 7. Recurrent Sequences in Finite Fields and Linear Cyclic Codes. 8. Finite Fields and Discreate Mathematics. 9. Congruences. 10. Some Related Problems. Appendix 1.
 Appendix 2.
 Appendix 3. Addendum. References. Index.
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 Koni͡agin, S. V. (Sergeĭ Vladimirovich)
 Cambridge : Cambridge University Press, 1999.
 Description
 Book — viii, 163 p. ; 24 cm.
 Summary

 Part I. Preliminaries: 1. Introduction
 2. Notation and auxiliary results
 Part II. Bounds of Character Sums: 3. Bounds of long character sums
 4. Bounds of short character sums
 5. Bounds of character sums for almost all moduli
 6. Bounds of Gaussian sums
 Part III. Multiplicative Translations of Sets: 7. Multiplicative translations of subgroups of F*p
 8. Multiplicative translations of arbitrary sets modulo p
 Part IV. Applications to Algebraic Number Fields: 9 Representatives of residue classes
 10. Cyclotomic fields and Gaussian periods
 Part V. Applications to Pseudorandom Number Generators: 11. Prediction of pseudorandom number generators
 12. Congruential pseudorandom number generators
 Part VI. Applications to Finite Fields: 13. Small mth roots modulo p
 14. Supersingular hyperelliptic curves
 15. Distribution of powers of primitive roots
 16. Difference sets in Vp
 17. Dimension of BCH codes
 18. An enumeration problem in finite fields.
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QA246.7 .K66 1999  Available 
 Koni͡agin, S. V. (Sergeĭ Vladimirovich)
 Cambridge ; New York : Cambridge University Press, 1999.
 Description
 Book — 1 online resource (viii, 163 pages) Digital: data file.
 Summary

 Part I. Preliminaries: 1. Introduction
 2. Notation and auxiliary results
 Part II. Bounds of Character Sums: 3. Bounds of long character sums
 4. Bounds of short character sums
 5. Bounds of character sums for almost all moduli
 6. Bounds of Gaussian sums
 Part III. Multiplicative Translations of Sets: 7. Multiplicative translations of subgroups of F*p
 8. Multiplicative translations of arbitrary sets modulo p
 Part IV. Applications to Algebraic Number Fields: 9 Representatives of residue classes
 10. Cyclotomic fields and Gaussian periods
 Part V. Applications to Pseudorandom Number Generators: 11. Prediction of pseudorandom number generators
 12. Congruential pseudorandom number generators
 Part VI. Applications to Finite Fields: 13. Small mth roots modulo p
 14. Supersingular hyperelliptic curves
 15. Distribution of powers of primitive roots
 16. Difference sets in Vp
 17. Dimension of BCH codes
 18. An enumeration problem in finite fields.
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 AAECC14 (2001 : Melbourne, Vic.)
 Berlin : Springer, 2001.
 Description
 Book — xii, 398 p. : ill. ; 24 cm.
 Summary

This book constitutes the refereed proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and ErrorCorrecting Codes, AAECC14, held in Melbourne, Australia in November 2001. The 36 revised full papers presented together with four invited papers were carefully reviewed and selected from 61 submissions. The papers are organized in topical sections on block codes, code constructions, codes and algebra  rings and fields, codes and algebra  algebraic geometry codes, sequences, cryptography, algorithms, algorithms  decoding, and algebraic constructions.
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SAL3 (offcampus storage)
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QA268 .A34 14TH 2001  Available 
 AAECC14 (2001 : Melbourne, Vic.)
 Berlin ; New York : Springer, 2001.
 Description
 Book — 1 online resource (xii, 398 pages) : illustrations Digital: text file.PDF.
 Summary

 Invited Contributions
 The Ubiquity of ReedMuller Codes
 Selfdual CodesTheme and Variations
 Design of Differential SpaceTime Codes Using Group Theory
 Ideal ErrorCorrecting Codes: Unifying Algebraic and NumberTheoretic Algorithms
 Block Codes
 Selfdual Codes Using Image Restoration Techniques
 Low Complexity TailBiting Trellises of Selfdual codes of Length 24, 32 and 40 over GF(2) and Z4 of Large Minimum Distance
 F q Linear Cyclic Codes over F q m: DFT Characterization
 Code Constructions
 Cyclic Projective ReedMuller Codes
 Codes Identifying Sets of Vertices
 Duality and Greedy Weights of Linear Codes and Projective Multisets
 Codes and Algebra:Rings and Fields
 Type II Codes over IF2r
 On Senary Simplex Codes
 Optimal Double Circulant Z4Codes
 Constructions of Codes from Number Fields
 On Generalized Hamming Weights for Codes over Finite Chain Rings
 Information Rates and Weights of Codes in Structural Matrix Rings
 Codes and Algebra:Algebraic Geometry Codes
 On Hyperbolic Codes
 On Fast Interpolation Method for GuruswamiSudan List Decoding of OnePoint AlgebraicGeometry Codes
 Computing the Genus of a Class of Curves
 Sequences
 Iterations of Multivariate Polynomials and Discrepancy of Pseudorandom Numbers
 Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation
 On the Nonexistence of (Almost )Perfect Quaternary Sequences
 Maximal Periods of x2 + c in Fq
 On the Aperiodic Correlation Function of Galois Ring mSequences
 Euclidean Modules and Multisequence Synthesis
 Cryptography
 On Homogeneous Bent Functions
 Partially Identifying Codes for Copyright Protection
 On the Generalised Hidden Number Problem and Bit Security of XTR
 CRYPTIM: Graphs as Tools for Symmetric Encryption
 Algorithms
 An Algorithm for Computing Cocyclic Matrices Developed over Some Semidirect Products
 Algorithms for Large Integer Matrix Problems
 On the Identification of Vertices and Edges Using Cycles
 Algorithms:Decoding
 On Algebraic Soft Decision Decoding of Cyclic Binary Codes
 Lifting Decoding Schemes over a Galois Ring
 Sufficient Conditions on Most Likely Local Subcodewords in Recursive Maximum Likelihood Decoding Algorithms
 A Unifying SystemTheoretic Framework for ErrorsandErasures ReedSolomon Decoding
 An Algorithm for Computing Rejection Probability of MLD with Threshold Test over BSC
 Algebraic Constructions
 Cartan's Characters and Stairs of Characteristic Sets
 On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2
 Algebraic Constructions for PSK SpaceTime Coded Modulation.
 Koni͡agin, S. V. (Sergeĭ Vladimirovich)
 Cambridge ; New York : Cambridge University Press, 1999.
 Description
 Book — viii, 163 p.
 Summary

 Part I. Preliminaries: 1. Introduction
 2. Notation and auxiliary results
 Part II. Bounds of Character Sums: 3. Bounds of long character sums
 4. Bounds of short character sums
 5. Bounds of character sums for almost all moduli
 6. Bounds of Gaussian sums
 Part III. Multiplicative Translations of Sets: 7. Multiplicative translations of subgroups of F*p
 8. Multiplicative translations of arbitrary sets modulo p
 Part IV. Applications to Algebraic Number Fields: 9 Representatives of residue classes
 10. Cyclotomic fields and Gaussian periods
 Part V. Applications to Pseudorandom Number Generators: 11. Prediction of pseudorandom number generators
 12. Congruential pseudorandom number generators
 Part VI. Applications to Finite Fields: 13. Small mth roots modulo p
 14. Supersingular hyperelliptic curves
 15. Distribution of powers of primitive roots
 16. Difference sets in Vp
 17. Dimension of BCH codes
 18. An enumeration problem in finite fields.
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 Providence, Rhode Island : American Mathematical Society, [2016]
 Description
 Book — viii, 238 pages : illustrations ; 26 cm.
 Summary

 * Lettre a Armand Borel by JP. Serre* Motivic Serre group, algebraic SatoTate group and SatoTate conjecture by G. Banaszak and K. S. Kedlaya* An application of the effective SatoTate conjecture by A. Bucur and K. S. Kedlaya* SatoTate groups of some weight 3 motives by F. Fite, K. S. Kedlaya, and A. V. Sutherland* SatoTate groups of $y^2=x^8+c$ and $y^2=x^7cx$ by F. Fite and A. V. Sutherland* Computing HasseWitt matrices of hyperelliptic curves in average polynomial time, II by D. Harvey and A. V. Sutherland* Quickly constructing curves of genus 4 with many points by E. W. Howe* Variants of the SatoTate and LangTrotter conjectures by K. James* On the distribution of the trace in the unitary symplectic group and the distribution of Frobenius by G. Lachaud* Lowerorder biases in elliptic curve Fourier coefficients in families by B. Mackall, S. J. Miller, c. Rapti, and K. Winsor.
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Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA251.5 .F76 2016  Unknown 
 New York, NY : Springer, ©2013.
 Description
 Book — 1 online resource Digital: text file.PDF.
 Summary

 Life and Mathematics of Alfred Jacobus van der Poorten (19422010) / David Hunt
 RamanujanSatoLike Series / Gert Almkvist, Jesús Guillera
 On the Sign of the Real Part of the Riemann Zeta Function / Juan Arias de Reyna, Richard P. Brent, Jan van de Lune
 Additive Combinatorics: With a View Towards Computer Science and CryptographyAn Exposition / Khodakhast Bibak
 Transcendence of Stammering Continued Fractions / Yann Bugeaud
 Algebraic Independence of Infinite Products and Their Derivatives / Peter Bundschuh
 Small Representations by Indefinite Ternary Quadratic Forms / J.B. Friedlander, H. Iwaniec
 Congruences for Andrews' sptFunction Modulo 32760 and Extension of Atkin's HeckeType Partition Congruences / F.G. Garvan
 Continued Fractions and Dedekind Sums for Function Fields / Yoshinori Hamahata
 Burgess's Bounds for Character Sums / D.R. HeathBrown
 Structured Hadamard Conjecture / Ilias S. Kotsireas
 Families of Cubic Thue Equations with Effective Bounds for the Solutions / Claude Levesque, Michel Waldschmidt
 Consequences of a Factorization Theorem for Generalized Exponential Polynomials with Infinitely Many Integer Zeros / Ouamporn Phuksuwan, Vichian Laohakosol
 On Balanced Subgroups of the Multiplicative Group / Carl Pomerance, Douglas Ulmer
 Some Extensions of the Lucas Functions / E.L. Roettger, H.C. Williams, R.K. Guy
 The Impact of Number Theory and ComputerAided Mathematics on Solving the Hadamard Matrix Conjecture / Jennifer Seberry
 Description of Generalized Continued Fractions by Finite Automata / Jeffrey Shallit
 On Prime Factors of Terms of Linear Recurrence Sequences / C.L. Stewart
 Some Notes on Weighted Sum Formulae for Double Zeta Values / James Wan
 Period(d)ness of LValues / Wadim Zudilin.
 International Conference on Finite Fields and Applications (8th : 2007 : Melbourne, Vic.)
 Providence, R.I. : American Mathematical Society, c2008.
 Description
 Book — viii, 265 p. : ill. ; 26 cm.
 Summary

 Analysis and optimization of ellipticcurve singlescalar multiplication by D. J. Bernstein and T. Lange On influences of Boolean variables and their computation by S. Boztas Subsequences of Sidelnikov sequences by N. Brandstatter and A. Winterhof A multilevel blocking distinctdegree factorization algorithm by R. P. Brent and P. Zimmermann New bounds on some parameters in the Waring problem for polynomials over a finite field by M. Car Dickson polynomial permutations by M. Cipu and S. D. Cohen Ring theoretic study of linear codes using additive polynomials by V. Deolalikar Toward a complete twin primes theorem for polynomials over finite fields by G. Effinger On the distribution of the elliptic curve power generator by E. ElMahassni and I. E. Shparlinski Discrete logarithms in curves over finite fields by A. Enge Some remarks on the HasseArf theorem by A. Garcia and H. Stichtenoth character sums for sequences of iterations of Dickson polynomials by D. Gomez and A. Winterhof What can be used instead of a Barker sequence? by J. Jedwab Order dividing extension fields and the root computation problem by A. M. Johnston Kasami bent functions are not equivalent to their duals by P. Langevin, G. Leander, and G. McGuire Reduced linear modular systems by E. Orozco Cocyclic Butson Hadamard matrices and codes over $\mathbb{Z}_n$ via the trace map by N. Pinnawala and A. Rao Dickson permutation polynomials that decompose in cycles of the same length by I. M. Rubio, G. L. Mullen, C. Corrada, and F. N. Castro Equidistribution of roots of $L$function of Gold exponential sum by V. K. Murty and K. W. Shum The simplex code over Galois rings by H. TapiaRecillas Finite fields and Galois geometries by J. A. Thas.
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QA247.3 .I58 2007  Available 
 Celebrating 75 Years of Mathematics of Computation (2018: Providence, R.I.), author.
 Providence, Rhode Island : American Mathematical Society, [2020]
 Description
 Book — 1 online resource (pages cm.)
 Summary

 Adaptive lowrank approximations for operator equations: Accuracy control and computational complexity / Markus Bachmayr and Wolfgang Dahmen
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15151 The PragerSynge theorem in reconstruction based a posteriori error estimation / Fleurianne Bertrand and Daniele Boffi
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15152 Linear and nonlinear fractional elliptic problems / Juan Pablo Borthagaray, Wenbo Li and Ricardo H. Nochetto
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15145 Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters / Ronald Cools, Frances Y. Kuo, Dirk Nuyens and Ian H. Sloan
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15150 Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues / Qiang Du, Bjorn Engquist and Xiaochuan Tian
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15175 The Stokes complex: A review of exactly divergencefree finite element pairs for incompressible flows / Michael Neilan
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15142 Finite element methods for Maxwell's equations / Peter Monk and Yangwen Zhang
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15143 Partial differential equation regularization for supervised machine learning / Adam M. Oberman
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15153 Iterative methods for linear systems of equations: A brief historical journey / Yousef Saad
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15141 The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems / Jie Shen and Xiaofeng Yang
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15147 A class of boundpreserving high order schemes: The main ideas and recent developments / ChiWang Shu
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15140 BDDC domain decomposition algorithms / Olof B. Widlund
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15146 Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields / Perlas Caranay, Matthew Greenberg and Renate Scheidler
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15148 A new ranking function for polynomial selection in the number field sieve / Nicolas David and Paul Zimmermann
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15139 A nilpotent quotient algorithm for finitely presented associative $\mathbb {Z}$algebras and its application to integral group rings / Bettina Eick and Tobias Moede
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15144 A tale of two omegas / Michael J. Mossinghoff and Timothy S. Trudgian
 https://www.ams.org/conm/754/ https://doi.org/10.1090/conm/754/15149
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 Berlin ; Boston : De Gruyter, [2013]
 Description
 Book — 1 online resource (285 p). Digital: text file; PDF.
 Summary

 Frontmatter
 Preface
 Contents
 Character Sums and Polyphase Sequence Families with Low Correlation, Discrete Fourier Transform (DFT), and Ambiguity / Gong, Guang
 Measures of Pseudorandomness / Gyarmati, Katalin
 Existence Results for Finite Field Polynomials with Specified Properties / Huczynska, Sophie
 Incidence Structures, Codes, and Galois Geometries / Jungnickel, Dieter
 Special Mappings of Finite Fields / Kyureghyan, Gohar M.
 On The Classification of Perfect Nonlinear (PN) and Almost Perfect Nonlinear (APN) Monomial Functions / Hernando, Fernando / McGuire, Gary
 Finite Fields and Quasirandom Points / Niederreiter, Harald
 Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects / Ostafe, Alina
 Additive Combinatorics over Finite Fields: New Results and Applications / Shparlinski, Igor E.
 Index
 Backmatter
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This book contains nine survey papers on topics in finite fields and their applications, in particular on character sums and polynomials. The articles are based on the invited talks ofa RicamWorkshop held at the St. Wolfgang Federal Institute for Adult Education in Strobl, Austria, September 27, 2012, by the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences.
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