Martino Borello

Université Paris 8, LAGA

Équipe AGAA

E-mail: surname @math.univ-paris13.fr (research), name.surname @univ-paris8.fr (teaching)
Office: D316 (Paris 13), A141-MR111 (Paris 8)

Detailed cv.

Short cv.

Discrete structures, like linear codes or lattices, actions of groups, as the symmetric groups on codes or group of matrices on families of lattices, and applications to Number Theory, Geometry and Information Theory. These are the key words of my research up to now, my expertise and my taste.

Preprints :

• On the algebraic structure of quasi group codes (with W. Willems), submitted
• A geometric characterization of minimal codes and their asymptotic performance (with G. N. Alfarano and A. Neri), submitted
• A note on linear complementary pairs of group codes (with J. de la Cruz and W. Willems), submitted
• Group codes over fields are asymptotically good (with W. Willems), submitted
• The Möbius function of PSL(3,2^p) for any prime p (with F. dalla Volta and G. Zini), submitted
• On checkable codes in group algebras (with J. de la Cruz and W. Willems), submitted
• The concatenated structure of quasi-abelian codes (with C. Güneri, E. Saçikara and P. Solé), submitted

Publications (in reverse chronological order) :

• Asymptotic performance of metacyclic codes (with P. Moree and P. Solé), to appear in Discrete Mathematics
• Minimal linear codes arising from blocking sets (with M. Bonini), Journal of Algebraic Combinatorics (2020)
• Symmetries of weight enumerators and applications to Reed-Muller codes (with O. Mila), Advances in Mathematics of Communications 13 (2): 313-328 (2019)
• Some new results on the the self-dual [120,60,24] code (with J. de la Cruz), Finite Fields and Their Applications 50: 17-34 (2018)
• Inhomogeneous minima of mixed signature lattices (with E. Bayer-Fluckiger and P. Jossen), Journal of Number Theory 167: 88-103 (2016)
• On involutions in extremal self-dual codes and the dual distance of semi self-dual codes (with G. Nebe), Finite Fields and Their Applications 33: 80-89 (2015)
• On the automorphism groups of binary linear codes, Topics in Finite Fields, Contemporary Mathematics 632 (2015)
• The automorphism group of a self-dual [72,36,16] code is not an elementary abelian group of order 8, Finite Fields and Their Applications 25: 1-7 (2014)
• The automorphism group of a self-dual [72,36,16] code does not contain S_3, A_4 or D_8 (with F. Dalla Volta and G. Nebe), Advances in Mathematics of Communications 7 (4): 503-510 (2013)
• Automorphisms of order 2p in binary self-dual extremal codes of length a multiple of 24 (with W. Willems), IEEE Transactions on Information Theory 59 (6): 3378-3383 (2013)
• The automorphism group of a self-dual [72,36,16] code does not contain elements of order 6, IEEE Transactions on Information Theory 58 (12): 7240-7245 (2012)

Other texts :

• Automorphism groups of self-dual binary linear codes with a particular regard to the extremal case of length 72 (PhD Thesis)
• Gauss class number problem: solution through the theory of L-function associated to elliptic curves (Msc Thesis - in Italian)
• Algebraic integers in complex quadratic fields (Bsc Thesis - in Italian)
• Medaglie Fields 2014 - Storie di matematici esemplari (Informative paper)
• On the stabilizer of weight enumerators of linear codes (with O.Mila)

Seminar organized :

• Séminaire Mathématiques Discrètes, Codes et Cryptographie

Courses :

• A.Y. 2019-2020: Combinatoire
• A.Y. 2019-2020: Codes correcteurs 1
• A.Y. 2019-2020: Algèbre 3
• A.Y. 2019-2020: Algèbre 2
• A.Y. 2019-2020: Introduction aux codes correcteurs
• A.Y. 2019-2020: Interactions codes-crypto
• A.Y. 2018-2019: Algèbre 3
• A.Y. 2018-2019: Combinatoire
• A.Y. 2018-2019: Codes correcteurs 1
• A.Y. 2018-2019: Introduction aux codes correcteurs
• A.Y. 2018-2019: Interactions codes-crypto
• A.Y. 2018-2019: Mathématiques et théorie de l'information
• A.Y. 2017-2018: Codes correcteurs 1
• A.Y. 2017-2018: Combinatoire
• A.Y. 2017-2018: Introduction aux codes correcteurs
• A.Y. 2017-2018: Interactions codes-crypto
• A.Y. 2017-2018: Mathématiques et théorie de l'information
• A.Y. 2016-2017: Combinatoire
• A.Y. 2016-2017: Géométrie
• A.Y. 2016-2017: Mathématiques et théorie de l’information
• A.Y. 2016-2017: Algorithmes pour la cryptographie
• A.Y. 2015-2016: Anneaux et corps (T.A. of Prof. Eva Bayer-Fluckiger)
• A.Y. 2015-2016: Théorie des groupes (T.A. of Prof. Eva Bayer-Fluckiger)
• A.Y. 2014-2015: Algèbre I-II (T.A. of Prof. Eva Bayer-Fluckiger)
• A.Y. 2013-2014: Recalls of Mathematics
• A.Y. 2013-2014: Istituzioni di matematiche (T.A. of Prof. Marina Avitabile)
• A.Y. 2012-2013: Algebraic topics for computer science (T.A. of Prof. Francesca Dalla Volta)
• A.Y. 2012-2013: Recalls of Mathematics

Some supervised projects:

• Inverse Galois problem : Intersective polynomials
  Semester Project - M1 - of Alessandro Slamitz (Automn 2014)
• Invariance for weight enumerators of evaluation codes and counting Fq-rational points on hypersurfaces
  Master Project - M2 - of Olivier Mila (Spring 2015)
• On the ideal class group of a number field
  Semester Project - L3 - of Filip Fifka (Automn 2015)
• Sur les groupes simples
  Semester Project - L3 - of Quentin Levêque (Spring 2016)
• Les codes en métrique rang
  Semester Project - M1 - of Omar Dianka (Spring 2018)
• Les bornes des codes correcteurs
  Semester Project - M1 - of Sarah Grib and Hassen Tazaïrt (Spring 2019)
• Side channel attack sur un cryptosysteme post quantique
  Master Project - M2 - of Yulliwas Ameur (Spring 2019)

Useful links :

• arXiv
• MathOverflow
• MathSciNet
• Emmeciquadro
• Online LaTeX Editor ShareLaTeX