Arithmetic, Geometry, Cryptography and Coding Theory.

This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18-22, 2015. Since the first meeting almost 30 years ago, the bienni...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Bassa, Alp
Otros Autores: Couvreur, Alain, Kohel, David
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2017.
Colección:Contemporary Mathematics.
Temas:
Coding theory > Congresses.
Geometry, Algebraic > Congresses.
Cryptography > Congresses.
Number theory > Congresses.
Information and communication, circuits > Theory of error-correcting codes and error-detecting codes > Geometric methods (including applications of algebraic geometry)
Géométrie algébrique > Congrès.
Cryptographie > Congrès.
Théorie des nombres > Congrès.
Coding theory
Cryptography
Geometry, Algebraic
Number theory
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover; Title page; Contents; Preface; The exact limit of some cubic towers; 1. Introduction; 2. Various Cubic Towers; 3. The Exact Genus and Exact Limit of Tower \GG; 4. Conclusion; Acknowledgment; References; Error-correction capability of Reed-Muller codes; 1. Introduction; 2. Presentation; 3. The results; 4. Proof of Theorem 3.1. Decoding a large number of errors; 5. The error correction capability function; 6. Note; References; Optimal and maximal singular curves; 1. Introduction; 2. Hallouin-Perret's approach; 3. Number of closed points of degree 2; 4. Genera spectrum of maximal curves.
  • On some bounds for symmetric tensor rank of multiplication in finite fields1. Introduction; 2. New upper bounds for the symmetric bilinear complexity; 3. Note on some unproven bounds; Acknowledgment; References; Codes from Jacobian surfaces; 1. Introduction; 2. Curves on abelian surfaces over finite fields; 3. Codes from Jacobian surfaces; 4. Some numerical results; Acknowledgments; References; A new proof of a Thomae-like formulafor non hyperelliptic genus 3 curves; 1. Introduction; 2. Review on Aronhold sets, fundamental systems and Riemann-Jacobi formula; 3. Proofs of Weber's formula.
  • AcknowledgmentReferences; Remarks on the Tsfasman-Boguslavsky Conjecture and higher weights of projective Reed-Muller codes; 1. Introduction; 2. Preliminaries; 3. TBC for Systems of Three Polynomial Equations; 4. Projective Reed-Muller codes and their higher weights; 5. A Counterexample to the TBC; Acknowledgment; References; Secret sharing schemes with strong multiplication and a large number of players from toric varieties; 1. Introduction; 2. Preliminaries; 3. Linear secret sharing schemes with multiplication on tori.
  • 4. Toric surfaces and linear secret sharing schemes with strong multiplicationReferences; Field extensions and index calculus on algebraic curves; 1. Introduction; 2. Index calculus and the divisor class group; 3. Known index calculus methods; 4. The general case; 5. Conclusion; References; Back Cover.

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