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 primarily work in algebraic coding theory, finite geometry, and combinatorics. My early research focused on self-dual codes and their automorphisms, with a particular emphasis on extremal codes. Currently, my work explores mainly G-codes (quasi-cyclic codes with additional symmetries), minimal and intersecting codes, and rank-metric codes. These families exhibit intriguing connections with other areas of mathematics, such as representation theory, finite geometry, and combinatorics, as well as potential applications in cryptography. Throughout my academic career, I have also been interested in problems related to Euclidean lattices, the Möbius function of subgroups, and the arithmetic of finite fields.

Teaching: Teaching page

Preprints:

A geometric invariant of linear rank-metric codes (with V. Astore, M. Calderini and F. Salizzoni), submitted
Left ideal LRPC codes and a ROLLO-type cryptosystem based on group algebras (with P. Santonastaso and F. Zullo), extended abstract, ALCOCRYPT conference (2023)

Publications (in reverse chronological order):

Dihedral Quantum Codes (with A.-L. Horlemann, H. Islam and N. Willenborg), to appear in Journal of Algebra and its Applications (2025)
The geometry of covering codes in the sum-rank metric (with M. Bonini and E. Byrne), to appear in Designs, Codes and Cryptography (2025)
The geometry of intersecting codes and applications to additive combinatorics and factorization theory (with W. Schmid and M. Scotti), to appear in Journal of Combinatorial Theory, Series A (2025)
Outer strong blocking sets (with G.N. Alfarano and A. Neri), The Electronic Journal of Combinatorics (2024)
Saturating linear sets of minimal rank (with D. Bartoli and G. Marino), Finite Fields and Their Applications, 95, 102390 (2024)
Geometric dual and sum-rank minimal codes (with F. Zullo), Journal of Combinatorial Designs, 32(5), 238-273 (2024)
Twisted skew G-codes (with A. Behajaina, J. de la Cruz and W. Willems), Designs, Codes and Cryptography, 92(6), 1803-1821 (2024)
Saturating systems and rank covering radius (with M. Bonini and E. Byrne), Journal of Algebraic Combinatorics, 58(4), 1173-1202 (2023)
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)