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Finite Fields.
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. Co...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
1994.
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| Colección: | Contemporary Mathematics Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Contents; Preface; Contributors; Conference Participants; Tools for coset weight enumerators of some codes; Algebraic decoding of cyclic codes: A polynomial ideal point of view; Polynomial factorisation, graphs, designs and codes; Character sums as orthogonal eigenfunctions of adjacency operators for Cayley graphs; Combinatorial cryptosystems galore!; A family of cryptosystems based on combinatorial properties of finite geometries; Global construction of general exceptional covers; Berlekamp's and Niederreiter's polynomial factorization algorithms.
- Hasse-Teichmiiller derivatives and products of linear recurring sequencesFactors of period polynomials for finite fields, II; A characterization of some ternary codes meeting the Griesmer bound; Projective geometry codes over prime fields; Codes over Eisenstein-Jacobi integers; Points on Fermat curves over finite fields; Lengths of factorizations for polynomials over a finite field; A note on Weil representation of SL2(Fq) and Soto-Andrade sums; Some sequences with good autocorrelation properties.
- Pellian equation conjecture and absolutely nonsingular projective varieties over a finite fieldâ#x80;#x93;Hecke operator and Pellian equation conjecture (IV)Strong pseudoprimes and generalized Carmichael numbers; Transformations of 4-regular graphs and equations over finite fields of Chevalley-Warning type; New examples of exceptional polynomials; New deterministic factorization algorithms for polynomials over finite fields; Discrete logarithms and smooth polynomials; Parents, children, neighbors and the shadow; The knapsack problem in cryptography.
- Iterated constructions of normal bases over finite fieldsPeriodicity properties of kth order linear recurrences whose characteristic polynomial splits completely over a finite field, I; Generalized Welch-Costas sequences and their application to Vatican arrays; Nonisomorphic complete sets of F-rectangles with varying numbers of symbols; A method of designing cellular automata as pseudorandom number generators for built-in self-test for VLSI; Finite ring sums from p-adic K-Bessel functions; On the Gross-Koblitz formula; New results on diagonal equations over finite fields from cyclic codes.