Riassunto
This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (University ofKarlsruhe), Stephen D. Cohen (University of Glasgow), Dieter Jungnickel (University of Augsburg, Chairman), Alfred Menezes (University of Waterloo), Gary L. Mullen (Pennsylvania State University), Ronald C. Mullin (University of Waterloo), Harald Niederreiter (Austrian Academy of Sciences), and Alexander Pott (University of Magdeburg). The program ofthe conference consisted offour full days and one halfday ofsessions, with 11 invited plenary talks andover80contributedtalks that re quired three parallel sessions. This documents the steadily increasing interest in finite fields and their applications. Finite fields have an inherently fasci nating structure and they are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields.
Contenuti
Projective Generalized Reed-Muller Codes over p-adic Numbers and Finite Rings by K.Abdukhalikov.- Towards a Basis for the Space of Regular Functions in a Tower of Function Fields Meeting the Drinfeld-Vladut Bound by I.Alshnikov, V.Deolalikar, P.V.Kumar, H.Stichtenoth.- Self-Dual Normal Bases and Related Topics by E.Bayer-Fluckiger.- Permutations amongst the Dembowski-Ostrom Polynomials by A.Blokhuis, R.S.Coulter, M.Henderson, C.M.O'Keefe.- Associative Rational Functions in Two Variables by J.V.Brawley, S.Gao and D.Mills.- A Note on the Minimal Polynomial of the Product of Linear Recurring Sequences by E.Cakcak.- Gelfond-Gramain's Theorem for Function Fields by M.Car.- On Generalized Bent and q-ary Perfect Nonlinear Functions by C.Carlet, S.Dubuc.- Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group by C.Cerroni, R.Hardo Schulz.- A Permutation of a Small Infinite Field by S.D.Cohen.- Almost Perfect Nonlinear Power Functions on GF(2n): A New Case for n Divisible by 5 by H.Dobbertin.- On Non-Abelian Semi-Regular Relative Difference Sets by D.Elvira, Y.Hiramine.- Applications of Arithmetical Geometry to Cryptographic Constructions by G.Frey.- Gauß Periods in Finite Fields by J.von zur Gathen, I.Shparlinski.- Construction of Orthomorphisms of Zn2 by S.W.Golomb, G.Gong, L.Mittenthal.- Period Polynomials for Fp2 of Fixed Small Degree by S.Gurak.- Universal Generators for Primary Closures of Galois Fields by D.Hachenberger.- Irreducible Polynomials Generated by Decimations by F. von Haeseler, W.Jürgensen.- Decoding Reed-Muller Codes beyond Half the Minimum Distance by A.E.Heydtmann, T.Jakobsen.- On Binary Cyclic Codes with Few Weights by H.D.L.Hollmann, Q. Xiang.- MacWilliams Identities for Linear Codes over Finite Frobenius Rings by T.Honold, I.Landjev.- Cyclotomic Function Fields with Many Rational Places by A.Keller.- On the Siamese Twin Designs by H.Kharaghani.- On the Brauer Monoid for Finite Fields by V.V.Kirichenko,B.V.Novikov.- Algorithms for Factoring Polynomials over Finite Fields by T.Lange, A.Winterhof.- Gauss Sums over Quasi-Frobenius Rings by P.Langevin, P.Sole.- On the Early History of Galois Fields by H.Lüneburg.- Linear Blocking Sets: a Survey by G.Lunardon, O.Polverino.- Comparison of Techniques on Divisibility Properties of Exponential Sums and Applications by O.Moreno and F.N.Castro.- On the Rank of Appearance and the Number of Zeros of the Lucas Sequences over Fq by S.Müller.- A Permutation Problem for Finite Fields by A.R.Prince.- The L-Function of Gold Exponential Sums by K.Shum, P.V.Kumar, T.Helleseth.- On Permutation Polynomials and Derivable Translation Planes by R.Vincenti.- Pure L-Functions from Algebraic Geometry of Finite Fields by D.Wan.- Incomplete Additive Character Sums and Applications by A.Winterhof.- Applications of Algebraic Curves to Constructions of Codes and Almost Perfect Sequences by C.Xing and H.Niederreiter.- Author Index
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