Martino Borello

Université Paris 8, LAGA, AGC3

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
• Evaluation of Forms for Distinguishing Rank-Metric Codes (with V. Astore, M. Calderini and F. Salizzoni), extended abstract, submitted to BFA 2025 (2025)
• 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), Journal of Combinatorial Theory, Series A, 214: 106023 (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)

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)

Coauthors:

Gianira N. Alfarano, Valentina Astore, Eva Bayer-Fluckiger, Daniele Bartoli, Angelot Benajaina, Matteo Bonini, Eimear Byrne, Marco Calderini, Francesca Dalla Volta, Javier de la Cruz, Cem Güneri, Anna-Lena Horlemann, Habibul Islam, Abdelillah Jamous, Peter Jossen, Giuseppe Marino, Olivier Mila, Pieter Moree, Gabriele Nebe, Alessandro Neri, Alberto Ravagnani, Elif Saçikara, Flavio Salizzoni, Paolo Santonastaso, Wolfgang Schmid, Martin Scotti, Patrick Solé, Wolfgang Willems, Nadja Willenborg, Giovanni Zini, Ferdinando Zullo,

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

• OpeRa 2024 in Caserta : Workshop "Open Problems on Rank-Metric Codes 2024"

• COSMO 2025 in Paris : Workshop "COmbinatorics of Spaces under MultiplicatiOn"

• Session Algebraic and Geometric Methods in Coding Theory within the SIAM Conference on Applied Algebraic Geometry

• Final Workshop Barracuda in Marseille : Final workshop "ANR algeBrA, pRoofs, pRotocols,Algorithms, Curves and sUrfaces for coDes and their Applications"

• OpeRa 2026 in Bordeaux : Workshop "Open Problems on Rank-Metric Codes 2026"

Useful links:

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