Papers and preprints
In memoriam Gilles Lachaud,
La Gazette des Mathématiciens, Société Mathématique de France,
Juillet 2018 - No. 157.
[0.1] Co-Editor with Gilles
Lachaud of the proceedings of the 2003 conference Arithmetic,
Geometry and Coding Theory, Société Mathématique de France,
Collection "Séminaires et congrès", no. 11, 2005: url.
[0.2] Co-Editor with Claude
Carlet, Philippe Langevin and Pascal Véron of a special issue of the
Springer journal Cryptography and
Communications - Discrete Structures, Boolean Functions and
Sequences, Volume 3, Number 4 / December 2011: special_issue.
[0.3] Co-Editor with
Christophe Ritzenthaler and Alexey Zykin of the proceedings of the
2011 conference Arithmetic,
Geometry, Cryptography and Coding Theory, Contemporary
Mathematics - Volume 574, American Mathematical Society 2012: content, url.
[0.4] Co-Editor with
Everett W. Howe and Christophe Ritzenthaler of the proceedings of
the 2017 conference Arithmetic
Geometry: Computation and Applications, Contemporary
Mathematics - Volume 722, American Mathematical Society 2019: url.
[0.5] Co-Editor with Pierre
Barthélémy and Nadia El Mrabet of the Special Issue from
Mathematics to Embedded Devices in Cryptography and
Communications, https://doi.org/10.1007/s12095-021-00502-1,
Springer 2021: url, pdf.
[1.1] Reed-Muller codes associated to projective algebraic
varieties, Lecture Notes in Mathematics 1518 Springer-Verlag,
Coding Theory and Algebraic Geometry, 4-17 (1991); (pdf).
[1.2] Algebraic geometric codes on surfaces, Conference at
Eurocode, Udine (Italie), (1992); in Ph.D. thesis of the University
of Aix-Marseille II, France (11/02/1993); HAL
preprint.
[1.3] Variétés sur un corps fini et codes géométriques
algébriques, Ph.D. thesis of the University of Aix-Marseille
II, France (11/02/1993), jury : Mireille Car, Patrick Delorme,
Gilles Lachaud, Mireille Martin-Deschamps, François Rodier
(referee), Mikhaïl Tsfasman (referee) and Jacques Wolfmann.
[1.4] A Weil theorem for singular curves, joint work with
Marc Perret, Arithmetic, Geometry and Coding Theory - 1993, Walter
de Gruyter, Berlin-New York, 1-7 (1996); (pdf).
[1.5] Coverings of singular curves over finite fields,
joint work with Marc Perret, Manuscripta Math.88, 467-478 (1995);
(pdf).
[1.6] Class number in totally imaginary extensions of totally
real function fields, Proceedings of the Third International
Conference on Finite fields and Applications, Lecture Note Series
of the London Mathematical Society, Cambridge University Press,
23-29 (1996); (pdf).
[1.7] Imaginary bicyclic biquadratic functions fields in
characteristic two, joint work with Dominique Le Brigand, J.
Number Theory 77, 36-50 (1999); (pdf).
[1.8] Variétés algébriques et corps de fonctions sur un corps
fini, Habilitation à Diriger des Recherches (13/12/2002),
jury : Gerhard Frey (referee), Gerard van der Geer (referee),
Gilles Lachaud, Eric Reyssat, Philippe Satgé, Mikhaïl Tsfasman,
Serge Vladut (referee); (pdf).
[1.9] Divisibility of zeta functions of curves in a covering,
joint work with Marc Perret, Archiv der Mathematik 82 (2004)
205-213; (pdf).
[1.10] On the characteristic polynomials of the Frobenius
endomorphism for projective curves over finite fields, joint
work with Marc Perret, Finite Fields and Their Applications 10/3
(2004) 412-431; (pdf).
[1.11] Class number in non Galois quartic and non abelian
Galois octic function fields, Bulletin of the Greek Math.
Soc., Vol. 52, 2006 (61-76); (pdf).
[1.12] On the weights of binary
irreducible cyclic codes, joint work with Philippe
Langevin, "Coding and Cryptography", Springer Lecture Notes in
Computer Science, volume
3969, pp 46-54 (2006); (pdf).
[1.13] On the semiprimitivity
of cyclic codes, joint work with Philippe Langevin,
Algebraic Geometry and its Applications, World Scientific, Series
on Number Theory and its Applications, vol. 5, pp 284-293 (2008);
(pdf).
[1.14] On some questions
related to the Gauss conjecture for function fields, joint work with Régis
Blache, Journal of Number Theory 128 (2008), no. 7,
2053-2062; (pdf).
[1.15] Differentially 4-uniform
functions, joint work with François Rodier, Comtemporary
Math. 521, pp 1-8 (2010) American Mathematical Society; (pdf).
[1.16] A few more functions
that are not APN infinitely often, joint work with Gary
McGuire and François Rodier, Comtemporary Math. 518,
pp 23-31 (2010) American Mathematical Society; (pdf).
[1.17] Vectorial solutions to list
multicoloring problems on graphs, joint work with
Jean-Christophe Godin and Olivier Togni, Advances and Applications
in Discrete Mathematics, Volume 9, Number 2, pp 65-81 (2012); (pdf).
[1.18] Sur le nombre de points
rationnels des variétés abéliennes et Jacobiennes sur les corps
finis, joint work with Safia Haloui and Gilles Lachaud, C.
R. Acad. Sci. Paris, Ser. I 350 (2012) 907–910; (pdf).
[1.19] On the number of points on
abelian and Jacobian varieties over finite
fields, joint work with Safia Haloui and Gilles Lachaud,
Acta Arithmetica 160.3, pp 201-242 (2013); (pdf).
[1.20] On a conjecture of
Helleseth, joint work with Philippe
Langevin, CAI 2013, LNCS 8080, pp. 113-118, 2013, Springer-Verlag
Berlin Heidelberg 2013; (pdf).
[1.21] Every triangle-free induced
subgraph of the triangular lattice is $(5m,2m)$-choosable,
joint work with Jean-Christophe Godin and Olivier Togni, Discrete
Applied Mathematics 166 (2014), 51-58; pdf.
[1.22] Cyclotomie des sommes de
Weil binomiales, joint work with Daniel J. Katz and
Philippe Langevin, C. R. Acad. Sci. Paris, Ser. I 352 (2014)
373-376; pdf.
[1.23] Cyclotomy of Weil sums of
binomials, joint work with Daniel J. Katz and Philippe
Langevin, Journal of Number Theory 154 (2015) 160-178; pdf.
[1.24] On the maximum number of
rational points on singular curves over finite fields,
joint work with Annamaria Iezzi, Moscow Math. Journal, Volume 15,
Issue 4, October-December 2015, pp. 615-627 (2015); website
; pdf.
[1.25] On the number of rational
points on Prym varieties
over finite fields, joint
work with Safia Haloui, Glasgow Math. Journal, Vol 58, 55-68
(2016); pdf.
[1.26] Free Choosability of the
cycle, joint work with Jean-Christophe Godin and Olivier
Togni, Graphs and Combinatorics, May 2016, Volume 32, pp.
851-859, Springer (2016) ; website;
pdf.
[1.27] Thue equations and
CM-fields, joint work with Dimitrios Poulakis,
Ramanujan Journal (2017) Volume 42, Issue 1, pp 145-156; pdf.
[1.28] Optimal and maximal
singular curves, joint work with Annamaria Iezzi,
Contemporary Mathematics, Volume 686, pp 31-43, American
Mathematical Society (2017); pdf.
[1.29] Hypersurfaces in weighted projective spaces over finite
fields with applications to coding theory, joint work with
Wouter Castryck, Sudhir R. Ghorpade, Gilles Lachaud, Michael E.
O'Sullivan and Samrith Ram, Algebraic Geometry for Coding
Theory and Cryptography, E.W. Howe et al. (eds), Springer
"Association for Women in Mathematics" series 9, DOI
10.1007/978-3-319-63931-4_2, pp 25-61 (2017); arXiv; (pdf).
[1.30] Differential uniformity and second order derivatives for
generic polynomials, joint work with Fabien Herbaut, Journal
of Pure and Applied Algebra 222 (2018), 1095-1110; pdf.
[1.31] Maximal differential uniformity polynomials, joint
work with Fabien Herbaut and José Felipe Voloch, Acta Arithmetica
188.4, pp 345-366 (2019); pdf.
[1.32] Algebraic geometry codes over abelian surfaces containing
no absolutely irreducible curves of low genus, joint work with
Elena Berardini, Fabien Herbaut and Marc Perret, (arXiv (2019); arXiv),
Finite Fields and Their Applications 70, pp. 1-20 (2021); pdf.
[1.33] Bounds on the minimum distance of algebraic geometry
codes defined over some families of surfaces, joint work with
Elena Berardini, Fabien Herbaut and Marc Perret, in Arithmetic,
Geometry, Cryptography and Coding Theory, Contemporary Mathematics,
vol. 770, Amer. Math. Soc., Providence, RI, 2021, pp. 11-28; pdf.
[1.34] Polynomials with maximal differential uniformity and the
exceptional APN conjecture, joint work with Fabien Herbaut and
Ali Issa, Journal of Algebra, Vol. 635, 1 December 2023, pp. 822-837
(2023) ; pdf.
[1.35] Closed points on curves over finite fields, joint
work with Fabien Herbaut and Julien Monaldi, submitted (2023) ; arXiv.
[1.36] Maximal number of rational points on hypersurfaces
in weighted projective spaces over finite fields, joint work
with Marc Perret, submitted (2024) ; arXiv.
[1.37] Trinomials with high differential uniformity, joint
work with Fabien Herbaut and Ali Issa, submitted (2024) ; arXiv.
[2.1] Algebraic geometric codes on surfaces, Conference at
Eurocode, Udine (Italie), (1992); in Ph.D. thesis of the University
of Aix-Marseille II, France (11/02/1993) ; HAL
preprint.
[2.2] On the weights of
irreducible cyclic codes, joint work with Philippe
Langevin, Book of Abstract of the Workshop on Coding and
Cryptography, Bergen (Norway), pp 161-169 (2005); (pdf)
[2.3] Extended core and
choosability of a graph, joint work with Jean-Christophe
Godin and Olivier Togni, (2010); arXiv preprint.
[3.1] Une formule de nombres de classes, Rapport de
Recherche S.D.A.D. - C.N.R.S. ESA 6081, (1998-3).
[3.2] Principal imaginary bicyclic function fields,
Rapport de Recherche S.D.A.D. - C.N.R.S. ESA 6081, (1998-4).
[3.3] An analogue of an Artin conjecture for zeta function
of algebraic curves, joint work with Marc Perret, Prétirage
de l'Institut de Mathématiques de Luminy no. 2002-25, (14 pages),
(2002).
[3.4] Asymptotic theory of
algebraic geometry codes,
preprint 2008-05 of the "Institut de Mathématiques de Toulon"
(2008).