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# Documents  Perret, Marc | enregistrements trouvés : 3

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## Algorithmic arithmetic, geometry, and coding theory.14th International Conference on arithmetic, geometry, cryptography and coding theoryMarseille # June 3-7, 2013 Ballet, Stéphane ; Perret, Marc ; Zaytsev, Alexey | American Mathematical Society 2015

Congrès

- v; 306 p.
ISBN 978-1-4704-1461-0

Contemporary mathematics , 0637

Localisation : Collection 1er étage

théorie des codes # géométrie algébrique # cryptographie # théorie des nombres

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## Towers of Ramanujan graphs Li, Winnie | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry;Number Theory

A $d$-regular graph is Ramanujan if its nontrivial eigenvalues in absolute value are bounded by $2\sqrt{d-1}$. By means of number-theoretic methods,infinite families of Ramanujan graphs were constructed by Margulis and independently by Lubotzky-Phillips-Sarnak in 1980's for $d=q+ 1$, where q is a prime power. The existence of an infinite family of Ramanujan graphs for arbitrary d has been an open question since then. Recently Adam Marcus, Daniel Spielman and Nikhil Srivastava gave a positive answer to this question by showing that any bipartite $d$-regular Ramanujan graph has a $2$-fold cover that is also Ramanujan. In this talk we shall discuss their approach and mentionsimilarities with function field towers. A $d$-regular graph is Ramanujan if its nontrivial eigenvalues in absolute value are bounded by $2\sqrt{d-1}$. By means of number-theoretic methods,infinite families of Ramanujan graphs were constructed by Margulis and independently by Lubotzky-Phillips-Sarnak in 1980's for $d=q+ 1$, where q is a prime power. The existence of an infinite family of Ramanujan graphs for arbitrary d has been an open question since then. Recently Adam Marcus, Daniel ...

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## Points rationnels sur les courbes sur un corps fini, sommes de caractères et codes correcteurs d'erreurs Perret, Marc | Université d'Aix Marseille 2 1990

Thèse

- 51 p.

Localisation : Ouvrage RdC (PERR)

Courbes algébriques sur un corps fini # borne de Weil # tours de corps de classes # fonctions L # Sommes de caractères # codes correcteurs d'erreurs # borne de Varshamov-Gilbert # empilements de sphères

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Ressources Electroniques (Depuis le CIRM)

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