The Fifth International Conference on Finite Fields and Applications Fq5 held at the University of Augsburg, Germany, from August 2-6, 1999 continued a series of biennial international conferences on finite fields. The proceedings document the steadily increasing interest in this topic. Finite fields have an inherently fascinating structure and 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. This interplay has always been a dominant theme in Fq conferences and was very much in evidence at Fq5. The proceedings reflect this, and offer an up-to-date collection of surveys and original research articles by leading experts in the area.
|Publisher:||Springer Berlin Heidelberg|
|Edition description:||Softcover reprint of the original 1st ed. 2001|
|Product dimensions:||6.10(w) x 9.25(h) x 0.04(d)|
Table of ContentsProjective 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