Page Web of Martino Borello

Martino Borello

Maître de conférences

Département de Mathématiques
2 rue de la Liberté
93526 Saint-Denis cedex
France

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

Detailed cv (updated on 20/03/2023).

Short cv (updated on 01/02/2021).

I work mainly in the field of algebraic coding theory. Several of my papers deal with self-dual codes and their automorphisms, with a particular focus on extremal codes. More recently, my research has focused on two families of linear codes, namely G-codes (which are quasi-cyclic codes with other symmetries) and minimal codes. Both families have interesting connections with other areas of mathematics, such as representation theory, finite geometry and combinatorics, as well as possible applications in cryptography. During my academic career, I have also been interested in problems on Euclidean lattices, on Möbius function of subgroups and on the arithmetic of finite fields.

Teaching : Teaching page

Preprints :

Saturating linear sets of minimal rank (with D. Bartoli and G. Marino), submitted
Geometric dual and sum-rank minimal codes (with F. Zullo), submitted
Outer strong blocking sets (with G.N. Alfarano and A. Neri), submitted
Twisted skew G-codes (with A. Behajaina, J. de la Cruz and W. Willems), submitted
Left ideal LRPC codes and a ROLLO-type cryptosystem based on group algebras (with P. Santonastaso and F. Zullo), extended abstract, submitted

Publications (in reverse chronological order) :

Saturating systems and rank covering radius (with M. Bonini and E. Byrne), to appear in Journal of Algebraic Combinatorics
Small strong blocking sets by concatenation (with D. Bartoli), SIAM Journal on Discrete Mathematics, 37(1): 65–82 (2023)
Linear cutting blocking sets and minimal codes in the rank metric (with G.N. Alfarano, A. Neri, and A. Ravagnani), Journal of Combinatorial Theory, Series A, 192: 105658 (2022)
On ideals in group algebras: an uncertainty principle and the Schur product (with W. Willems and G. Zini), Forum Mathematicum (2022)
On the algebraic structure of quasi group codes (with W. Willems), Journal of Algebra and its Applications, 2350222 (2022)
Three combinatorial perspectives on minimal codes (with G.N. Alfarano, A. Neri, and A. Ravagnani), SIAM Journal on Discrete Mathematics, 36(1): 461-489 (2022)
The uncertainty principle over finite fields (with P. Solé), Discrete Mathematics, 345(1): 112670 (2022)
A geometric characterization of minimal codes and their asymptotic performance (with G. N. Alfarano, and A. Neri), Advances in Mathematics of Communications, 16(1): 115-133 (2022)
On checkable codes in group algebras (with J. de la Cruz and W. Willems), Journal of Algebra and its Applications, 21(6): 2250125 (2022)
The concatenated structure of quasi-abelian codes (with C. Güneri, E. Saçikara, and P. Solé), Designs, Codes and Cryptography, 90:2647–2661 (2022)
Dihedral codes with prescribed minimum distance (with A. Jamous), In: Bajard J.C., Topuzoglu A. (eds) Arithmetic of Finite Fields. WAIFI 2020. Lecture Notes in Computer Science, vol 12542. Springer, Cham. (2021)
The Möbius function of PSL(3,2^p) for any prime p (with F. dalla Volta, and G. Zini), International Journal of Algebra and Computation, 31(6): 987-1011 (2021)
Minimal linear codes arising from blocking sets (with M. Bonini), Journal of Algebraic Combinatorics, 53(2): 327-341 (2021)
Group codes over fields are asymptotically good (with W. Willems), Finite Fields and Their Applications, 68: 101738 (2020)
A note on linear complementary pairs of group codes (with J. de la Cruz, and W. Willems), Discrete Mathematics, 343(8): 111905 (2020)
Asymptotic performance of metacyclic codes (with P. Moree and P. Solé), Discrete Mathematics, 343(7): 111885 (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)

Organization of :

Séminaire Mathématiques Discrètes, Codes et Cryptographie in Paris 8
Session Algebraic coding theory and cryptography within the 29th Nordic Congress of Mathematicians with EMS
Fq15 in Paris : International Conference on Finite Fields and Their Applications 2023

Useful links :