Contents

Preface vii

On the fourth moment of theta functions at their central point

Amadou D. Barry, Stephane

´

R. Louboutin 1

On the construction of Galois towers

Alp Bassa, Peter Beelen 9

Codes deﬁned by forms of degree 2 on quadric varieties in

P4(Fq

)

Fr´

ed

´

eric A. B. Edoukou 21

Curves of genus 2 with elliptic diﬀerentials and associated Hurwitz spaces

Gerhard Frey, Ernst Kani 33

A note on the Giulietti-Korchmaros maximal curve

Arnaldo Garcia 83

Subclose families, threshold graphs, and the weight hierarchy of Grassmann

and Schubert codes

Sudhir R. Ghorpade, Arunkumar R. Patil, Harish K. Pillai 87

Characteristic polynomials of automorphisms of hyperelliptic curves

Robert M. Guralnick, Everett W. Howe 101

Breaking the Akiyama-Goto cryptosystem

Petar Ivanov,

Jos´

e Felipe Voloch 113

Hyperelliptic curves, L-polynomials, and random matrices

Kiran S. Kedlaya, Andrew V. Sutherland 119

On special ﬁnite ﬁelds

Florian Luca, Igor E. Shparlinski 163

Borne sur le degr´ e des polynˆ omes presque parfaitement non-lin´eaires

Franc ¸ois Rodier 169

How to use ﬁnite ﬁelds for problems concerning inﬁnite ﬁelds

Jean-Pierre Serre 183

On the generalizations of the Brauer-Siegel theorem

Alexey Zykin 195

v