میدان‌های متناهی: نظریه، کاربردها و الگوریتم‌ها: کنفرانس بین‌المللی دوم درباره میدان‌های متناهی، 17-21 اوت 1993، لاس‌وگاس، نوادا

Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering. Readership: Graduate students and researchers in the theory and application of finite fields. More generally, students and researchers in algebra, number theory, combinatorial design theory, coding theory, and cryptology. Tools For Coset Weight Enumerators Of Some Codes / Pascale Charpin -- Algebraic Decoding Of Cyclic Codes: A Polynomial Ideal Point Of View / Xuemin Chen, I.s. Reed, T. Helleseth And T.k. Truong -- Polynomial Factorisation, Graphs, Designs And Codes / Stephen D. Cohen -- Character Sums As Orthogonal Eigenfunctions Of Adjacency Operators For Cayley Graphs / Ronald Evans -- Combinatorial Cryptosystems Galore! / Michael Fellows And Neal Koblitz -- A Family Of Cryptosystems Based On Combinatorial Properties Of Finite Geometries / Raul Figueroa, Pablo M. Salzberg And Peter Jau-shyong Shiue -- Global Construction Of General Exceptional Covers / Michael D. Fried -- Berlekamp's And Niederreiter's Polynomial Factorization Algorithms / Shuhong Gao And Joachim Von Zur Gathen -- Hasse-teichmuller Derivatives And Products Of Linear Recurring Sequences / Rainer Gottfert And Harald Niederreiter -- Factors Of Period Polynomials For Finite Fields, Ii / S. Gurak. A Characterization Of Some Ternary Codes Meeting The Griesmer Bound / Noboru Hamada And Tor Helleseth -- Projective Geometry Codes Over Prime Fields / J.w.p. Hirschfeld And R. Shaw -- Codes Over Eisenstein-jacobi Integers / Klaus Huber -- Points On Fermat Curves Over Finite Fields / Hubert Kiechle -- Lengths Of Factorizations For Polynomials Over A Finite Field / A. Knopfmacher, J. Knopfmacher And R. Warlimont -- A Note On Weil Representation Of Sl[subscript 2](f[subscript Q]) And Soto-andrade Sums / Jinghua Kuang -- Some Sequences With Good Autocorrelation Properties / Philippe Langevin -- Pellian Equation Conjecture And Absolutely Nonsingular Projective Varieties Over A Finite Field -- Hecke Operator And Pellian Equation Conjecture (iv) / Hongwen Lu -- Strong Pseudoprimes And Generalized Carmichael Numbers / Rex Matthews -- Transformations Of 4-regular Graphs And Equations Over Finite Fields Of Chevalley-warning Type / Oscar Moreno And Victor A. Zinoviev. New Examples Of Exceptional Polynomials / Peter Muller -- New Deterministic Factorization Algorithms For Polynomials Over Finite Fields / Harald Niederreiter -- Discrete Logarithms And Smooth Polynomials / A.m. Odlyzko -- Parents, Children, Neighbors And The Shadow / Vera Pless -- The Knapsack Problem In Cryptography / Minghua Qu And S.a. Vanstone -- Iterated Constructions Of Normal Bases Over Finite Fields / Alfred Scheerhorn -- Periodicity Properties Of Kth Order Linear Recurrences Whose Characteristic Polynomial Splits Completely Over A Finite Field, I / Lawrence Somer -- Generalized Welch-costas Sequences And Their Application To Vatican Arrays / Hong Y. Song And Solomon W. Golomb -- Nonisomorphic Complete Sets Of F-rectangles With Varying Numbers Of Symbols / Stephan J. Suchower -- A Method Of Designing Cellular Automata As Pseudorandom Number Generators For Built-in Self-test For Vlsi / Shu Tezuka And Masanori Fushimi -- Finite Ring Sums From P-adic K-bessel Functions / Cynthia E. Trimble. On The Gross-koblitz Formula / Paul Thomas Young -- New Results On Diagonal Equations Over Finite Fields From Cyclic Codes / Jacques Wolfmann -- Open Problems And Conjectures / Klaus Huber, Ilene H. Morgan, Gary L. Mullen, Harald Niederreiter, A. Odlyzko, Johan Van Tilburg And Daqing Wan. Second International Conference On Finite Fields : Theory, Applications, And Algorithms, August 17-21, 1993, Las Vegas, Nevada ; Gary L. Mullen, Peter Jau-shyong Shiue, Editors. Includes Bibliographical References. P. Charpin -- Tools for coset weight enumerators of some codes X. Chen, I. S. Reed, T. Helleseth, and T. K. Truong -- Algebraic decoding of cyclic codes: A polynomial ideal point of view S. D. Cohen -- Polynomial factorisation, graphs, designs and codes R. Evans -- Character sums as orthogonal eigenfunctions of adjacency operators for Cayley graphs M. Fellows and N. Koblitz -- Combinatorial cryptosystems galore! R. Figueroa, P. M. Salzberg, and P. J.-S. Shiue -- A family of cryptosystems based on combinatorial properties of finite geometries M. D. Fried -- Global construction of general exceptional covers S. Gao and J. von zur Gathen -- Berlekamp's and Niederreiter's polynomial factorization algorithms R. Göttfert and H. Niederreiter -- Hasse-Teichmüller derivatives and products of linear recurring sequences S. Gurak -- Factors of period polynomials for finite fields, II N. Hamada and T. Helleseth -- A characterization of some ternary codes meeting the Griesmer bound J. W. P. Hirschfeld and R. Shaw -- Projective geometry codes over prime fields K. Huber -- Codes over Eisenstein-Jacobi integers H. Kiechle -- Points on Fermat curves over finite fields A. Knopfmacher, J. Knopfmacher, and R. Warlimont -- Lengths of factorizations for polynomials over a finite field J. Kuang -- A note on Weil representation of SL2(Fq) and Soto-Andrade sums P. Langevin -- Some sequences with good autocorrelation properties H. Lu -- Pellian equation conjecture and absolutely nonsingular projective varieties over a finite field--Hecke operator and Pellian equation conjecture (IV) R. Matthews -- Strong pseudoprimes and generalized Carmichael numbers O. Moreno and V. A. Zinoviev -- Transformations of 4-regular graphs and equations over finite fields of Chevalley-Warning type P. Müller -- New examples of exceptional polynomials H. Niederreiter -- New deterministic factorization algorithms for polynomials over finite fields A. M. Odlyzko -- Discrete logarithms and smooth polynomials V. Pless -- Parents, children, neighbors and the shadow M. Qu and S. A. Vanstone -- The knapsack problem in cryptography A. Scheerhorn -- Iterated constructions of normal bases over finite fields L. Somer -- Periodicity properties of k th order linear recurrences whose characteristic polynomial splits completely over a finite field, I H. Y. Song and S. W. Golomb -- Generalized Welch-Costas sequences and their application to Vatican arrays S. J. Suchower -- Nonisomorphic complete sets of F-rectangles with varying numbers of symbols S. Tezuka and M. Fushimi -- A method of designing cellular automata as pseudorandom number generators for built-in self-test for VLSI C. E. Trimble -- Finite ring sums from p-adic K -Bessel functions P. T. Young -- On the Gross-Koblitz formula J. Wolfmann -- New results on diagonal equations over finite fields from cyclic codes K. Huber, I. H. Morgan, G. L. Mullen, H. Niederreiter, A. Odlyzko, J. van Tilburg, and D. Wan -- Open problems and conjectures Contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. This work covers topics such as theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory and algorithms related to finite fields.