UID:
almafu_9959239107602883
Umfang:
1 online resource (xx, 401 pages) :
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digital, PDF file(s).
ISBN:
1-139-88523-5
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1-107-36734-4
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1-107-37192-9
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1-107-36243-1
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1-107-36951-7
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1-299-40498-7
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1-107-36488-4
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0-511-52598-2
Serie:
London Mathematical Society lecture note series ; 233
Inhalt:
Finite fields are algebraic structures in which there is much research interest and they have been shown to have a wide range of applications. These proceedings give a state-of-the-art account of the area of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. These also demonstrate inter-connections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.
Anmerkung:
"Proceedings of the Third International Conference on Finite Fields and Applications held at the University of Glasgow, Scotland, 11-14 July, 1995"--Pref.
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Cover; Half-title; Title; Copyright; Contents; Preface; Conference Participants; Factorizations over finite fields Shreeram S Abhyankar; Section 1: Introduction; Section 2: Partitions of Roots of Unity; Section 3: Review of Classical Groups; Section 4: Genus Zero and Strong Genus Zero; Section 5: Further Generalized Artin Schreier Polynomials; Section 6: Again Generalized Artin Schreier Polynomials; Section 7: Deformations of the Symplectic Group Equations; Section 8: Permutation Polynomials; Section 9: The Mantra
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Class number in totally imaginary extensions of totally real fnnrtion fields Yves AubryIntroduction.; 1. Notation.; 2. Finiteness theorem.; Automorphism groups and permutation groups of affine-in variant codes Thierry P Berger; 1 Preliminaries; 1.1 Permutation groups and Automorphism groups ofa code.; 1.2 Indecomposable codes.; 1.3 Afflne-invariant codes.; 1.4 Extended primitive cyclic codes; 2 Automorphism group and permutationgroup of an affine-invariant code.; 2.1 Known results on permutation groups of affineinvariantcodes.
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2.2 Relations between permutation groups and automorphismgroups of affine-invariant codes.3 Codes equivalent to an affine-invariant code; 3.1 Equivalence of codes; 3.2 Extended cyclic codes equivalent toan affine-invariant code.; A construction of bent fund ions Claude Carlet; 1 Introduction; 2 The Construction; 3 Known classes of explicit bent functions; Monodromy groups of classical families over finite fields Stephen D Cohen and Rex W Matthews; 1. INTRODUCTION; 2. CLASSICAL FAMILIES WITH REGULAR GEOMETRIC MONODROMYGROUPS.; 3. NON-REGULAR MONODROMY GROUPS.
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Wan's bound for value sets of polynomials Thomas W Cusick and Peter MiillerComparative implementations of Berlekamp's and Niederreitor's polynomial factorization algorithms Peter Fleischmann and Peter Roelse; 1 Introduction; 2 Basic concepts; 2.1 Equivalent subspaces; 2.2 Extracting factors and randomization; 2.3 Berlekamp's and Niederreiter's Subspaces; 3 The implementations; 4 Concluding remarks; On the minimal polynomials for certain Gauss periods over finite fields S Gurak; 1. Introduction; 2. Determination of βQ(n).; 3. Some explicit formulas for the power series C(X)
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Completely free elements Dirk Hachenberger1. A Strengthening of the Normal Basis Theorem.; 2. The Existence of Completely Free Elements.; 3. Decompositions of Completely Free Elements.; 4. Regular Extensions.; 5. Explicit Constructions.; 6. Concluding Remarks.; Exponential sums over Galois rings and their applications T Helleseth, P V Kumar and A G Shanbhag; 1 Introduction; 2 Galois Rings; 3 Z4-linear codes; 4 Exponential sums; 4.1 The Weil-Carlitz-Uchiyama bound; 4.2 Exponential sums in Galois rings; 5 Applications to coding theory; 6 Application to sequence designs; 7 Conclusions
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Maximal sets of mutually orthogonal Latin squares Dieter Jungnickel
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English
Weitere Ausg.:
ISBN 0-521-56736-X
Sprache:
Englisch
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