Finite Fields and Applications

Table of Contents

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   Book Overview
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   Chapter 1 Projective Generalized Reed-Muller Codes over p -adic Numbers and Finite Rings
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   Chapter 2 Towards a Basis for the Space of Regular Functions in a Tower of Function Fields Meeting the Drinfeld-Vladut Bound
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   Chapter 3 Self-Dual Normal Bases and Related Topics
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   Chapter 4 Permutations amongst the Dembowski-Ostrom Polynomials
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   Chapter 5 Associative Rational Functions in Two Variables
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   Chapter 6 A Note on the Minimal Polynomial of the Product of Linear Recurring Sequences
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   Chapter 7 Gelfond-Gramain’s Theorem for Function Fields
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   Chapter 8 On Generalized Bent and q -ary Perfect Nonlinear Functions
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    Chapter 9 Divisible Designs Admitting, as an Automorphism Group, an Orthogonal Group or a Unitary Group
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    Chapter 10 A Permutation of a Small Infinite Field
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    Chapter 11 Almost Perfect Nonlinear Power Functions on GF(2 n ): A New Case for n Divisible by 5
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    Chapter 12 On Non-Abelian Semi-Regular Relative Difference Sets
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    Chapter 13 Applications of Arithmetical Geometry to Cryptographic Constructions
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    Chapter 14 Gauß Periods in Finite Fields
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    Chapter 15 Constructions of Orthomorphisms of ℤ 2 n
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    Chapter 16 Period Polynomials for $$ {F_{{{p^{2}}}}} $$ of Fixed Small Degree
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    Chapter 17 Universal Generators for Primary Closures of Galois Fields
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    Chapter 18 Irreducible Polynomials Generated by Decimations
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    Chapter 19 Decoding Reed-Muller Codes beyond Half the Minimum Distance
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    Chapter 20 On Binary Cyclic Codes With Few Weights
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    Chapter 21 MacWilliams Identities for Linear Codes over Finite Frobenius Rings
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    Chapter 22 Cyclotomic Function Fields with Many Rational Places
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    Chapter 23 On the Siamese Twin Designs
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    Chapter 24 On the Brauer Monoid for Finite Fields
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    Chapter 25 Algorithms for Factoring Polynomials over Finite Fields
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    Chapter 26 Gauss Sums over Quasi-Frobenius Rings
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    Chapter 27 On the Early History of Galois Fields
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    Chapter 28 Linear Blocking Sets: A Survey
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    Chapter 29 Comparison of Techniques on Divisibility Properties of Exponential Sums and Applications
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    Chapter 30 On the Rank of Appearance and the Number of Zeros of the Lucas Sequences over $$ {\mathbb{F}_{q}} $$
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    Chapter 31 A Permutation Problem for Finite Fields
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    Chapter 32 The L -Function of Gold Exponential Sum
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    Chapter 33 On Permutation Polynomials and Derivable Translation Planes
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    Chapter 34 Pure L -Functions from Algebraic Geometry over Finite Fields
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    Chapter 35 Incomplete Additive Character Sums and Applications
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    Chapter 36 Applications of Algebraic Curves to Constructions of Codes and Almost Perfect Sequences