I am currently a postdoctoral researcher in mathematics at Ghent University, funded by the Research Foundation Flanders (FWO).
Before, I was a postdoctoral researcher in the Nonlinear Algebra group lead by Prof. Bernd Sturmfels at the Max Planck Institute for Mathematics in the Sciences.
From 2019 to 2021 I was awarded with an Early Postdoc.Mobility Fellowship from the Swiss National Science Foundation, which I used jointly between INRIA Saclay, advised by Prof. Daniel Augot, and Technical Univerity of Munich, advised by Prof. Antonia Wachter-Zeh.
In the summer 2019 I got my PhD degree in Mathematics at University of Zurich, under the supervision of Prof.
Joachim Rosenthal.
My main research interest is Algebraic Coding Theory. I study the algebra of finite fields and its applications, with also a focus on combinatorial problems on codes. I am especially interested in rank-metric codes and their algebraic structures.
List of coauthors:
Tim L. Alderson,
Gianira N. Alfarano,
Noga Alon,
Daniel Augot,
Jessica Bariffi,
Daniele Bartoli,
Arthur Bik,
Anurag Bishnoi,
Tristram Bogart,
Martino Borello,
Eimear Byrne,
Alain Couvreur,
Shagnik Das,
Yassine El Maazouz,
Jos G mez Torrecillas,
Marvin Anas Hahn,
Lukas Holzbaur,
Anna-Lena Horlemann-Trautmann,
David Karpuk,
Julien Lavauzelle,
Hedongliang Liu,
Fco. Javier Lobillo Borrero,
Giuseppe Marino,
Sam Mattheus,
Giacomo Micheli,
Diego Napp,
Gabriel Navarro,
Sven Puchinger,
Tovohery Hajatiana Randrianarisoa,
Alberto Ravagnani,
Julian Renner,
Veronica Requena,
Johan Rosenkilde,
Joachim Rosenthal,
Paolo Santonastaso,
Davide Schipani,
John Sheekey,
Minjia Shi,
Vladimir Sidorenko,
Patrick Sol ,
Mima Stanojkovski,
Rocco Trombetti,
Mauricio Velasco,
Lara Vicino,
Antonia Wachter-Zeh.
Ferdinando Zullo.
News
Invited speaker for the workshop OpeRa 2024 - Caserta: Open Problems on Rank-Metric Codes which will be held on February 14-16 at University of Campania "L. Vanvitelli", Italy.
Co-organizer of the Coding Theory Colloquium, which will take place on November 8th, 2023 at Ghent University, Belgium.
Invited speaker for the Academy Contact Forum `Coding Theory and Cryptography IX' at the Royal Flemish Academy of Belgium for Science and the Arts.
Our paper on evasive subspaces and near MRD codes has been published in Discrete Mathematics. Check it out here.
Co-organizer of the session Coding Theory and Galois Geometries for the SIAM Conference on Applied Algebraic Geometry (AG23), 10-14 July 2023, Eindhoven University of Technology, The Netherlands.
Our preprint on a partial proof of the Etzion-Silberstein conjecture is on arXiv. Check it out here.
Our preprint on strong blocking sets from expander graphs is on arXiv. Check it out here. You can also read about it in this nice article on Anurag's Math blog
Our preprint on flag-rank metric codes is on arXiv. Check it out here.
Our preprint on symmetric rank-metric codes is on arXiv. Check it out here.
Our preprint on outer strong blocking sets is on arXiv. Check it out here.
Our paper on weighted convolutional Reed-Solomon codes has been published in Linear and Multilinear Algebra. Check it out here.
Our paper on one-weight codes in the sum-rank metric has been published in Journal of Combinatorial Theory, Series A. Check it out here.
Since October 2022, I am an FWO postdoctoral fellow at Ghent University.
My paper on twisted linearized Reed-Solomon code has been published in Journal of Algebra. Check it out here.
Invited speaker for the Algebraic Methods in Coding Theory and Communication workshop. Here the video of the talk.
Co-organizer of the Algebraic Coding Theory Summer School - ACT22, 4-8 July 2022, University of Zurich, Switzerland.
This nice article on Anurag's Math blog talks about our published paper!
Invited speaker for the Seminars on Cryptography and Coding Theory organized by Unione Matematica Italiana. Here the video of the talk (in Italian).
Department of mathematics: analysis, logic and discrete mathematics, Ghent University, Krijgslaan 281, S8, 9000 Gent
Research Activity
Journal Publications
Evasive subspaces, generalized rank weights and near MRD codes, with G. Marino and R. Trombetti, Discrete Mathematics, 346(12): 113605, 2023.
arXiv version
The geometry of one-weight codes in the sum-rank metric, with P. Santonastaso and F. Zullo, Journal of Combinatorial Theory Series A, 194: 105703, 2023.
arXiv version
Weighted Reed-Solomon convolutional codes, with G. N. Alfarano, D. Napp and V. Requena, Linear and Multilinear Algebra, 2023.
arXiv version
Twisted Linearized Reed-Solomon Codes: A Skew Polynomial Framework, Journal of Algebra, 609: 792-839, 2022.
arXiv version
New MRD codes from linear cutting blocking sets, with D. Bartoli and G. Marino, Annali di Matematica Pura ed Applicata, 2022.
arXiv version
Linear Cutting Blocking Sets and Minimal Codes in the Rank Metric, with G. N. Alfarano, M. Borello and A. Ravagnani, Journal of Combinatorial Theory, Series A, 192: 105658, 2022.
arXiv version
Moderate-Density Parity-Check Codes from Projective Bundles, with J. Bariffi, S. Mattheus and J. Rosenthal, Designs, Codes and Cryptography, 2022. arXiv version
Extending two families of maximum rank distance codes, with P. Santonastaso and F. Zullo, Finite Fields and Their Applications, 81: 102045, 2022. arXiv version
Sum-rank product codes and bounds on the minimum distance, with G. N. Alfarano, F. J. Lobillo and A. Wachter-Zeh, Finite Fields and their Applications, 80: 102013, 2022.
arXiv version
Three Combinatorial Perspectives on Minimal Codes, with G. N. Alfarano, M. Borello and A. Ravagnani, SIAM Journal on Discrete Mathematics, 36(1): 461-489, 2022.
arXiv version
Constructing Partial MDS Codes from Reducible Algebraic Curves, with T. Bogart, A.-L. Horlemann-Trautmann, D. Karpuk and M. Velasco, SIAM Journal on Discrete Mathematics, 35(4): 2946-2970, 2021.
arXiv version
Decoding of Interleaved Alternant Codes, with L. Holzbaur, H. Liu,
S. Puchinger, J. Rosenkilde, V. Sidorenko and A. Wachter-Zeh, IEEE Transactions on Information Theory, 67(12): 8016-8033, 2021.
arXiv version
Rank-metric codes over arbitrary Galois extensions and rank analogues of Reed-Muller codes, with D. Augot, A. Couvreur and J. Lavauzelle, SIAM Journal on Applied Algebra and Geometry, 5(2): 165-199, 2021.
arXiv version
Low-Rank Parity-Check Codes over Galois Rings, with J. Renner and S. Puchinger, Designs, Codes and Cryptography, 89: 351 386, 2021.
arXiv version
Roos bound for skew cyclic codes in Hamming and rank metric, with G. N. Alfarano and F. J. Lobillo,
Finite Fields and Their Applications, 69: 101772, 2021. arXiv version
A geometric characterization of minimal codes and their asymptotic performance, with G. N. Alfarano and M. Borello,
Advances in Mathematics of Communications, 16(1): 115-133, 2022. arXiv version
Equivalence and Characterizations of Linear Rank-Metric Codes Based on Invariants, with S. Puchinger and A.-L. Horlemann-Trautmann, Linear Algebra and its applications, 2020. arXiv version
How many weights can a quasi-cyclic code have?
with M. Shi and P. Sol , IEEE Transactions on Information Theory, 66(11): 6855-6862, 2020.
Systematic encoders for generalized Gabidulin codes and the q-analogue
of Cauchy matrices, Linear Algebra and its Applications, 593: 116-149, 2020.
Random construction of partial MDS codes, with A.-L. Horlemann-
Trautmann, Designs, Codes and Cryptography, 88: 711-725, 2020.
New Lower Bounds for Permutation Codes using Linear Block Codes,
with G. Micheli, IEEE Transactions on Information Theory, 66(7): 4019-4025, 2020.
How many weights can a cyclic code have?
with M. Shi, X. Li and P. Sol , IEEE Transactions on Information Theory, 66(3): 1449-1459, 2020. arXiv version
Tensor representation of rank-metric codes
with E. Byrne, A. Ravagnani and J. Sheekey, SIAM Journal on Applied Algebra and Geometry, 3(4): 614-643, 2019. arXiv version
A complete classification of partial-MDS (maximally recoverable) codes
with one global parity, with A.-L. Horlemann-Trautmann, Advances
in Mathematics of Communications, 14(1): 69-88, 2020. arXiv version
Maximum weight spectrum codes, with T. L. Alderson, Advances
in Mathematics of Communications, 13(1): 101-119, 2019. arXiv version
On the genericity of maximum rank distance and Gabidulin codes, with
A.-L. Horlemann-Trautmann, T. Randrianarisoa, and J. Rosenthal, Designs,
Codes and Cryptography, 86(2): 341-363, 2018. arXiv version
Hartmann-Tzeng bound and skew cyclic codes of designed Hamming
distance, with J. G mez-Torrecillas, F. J. Lobillo and G. Navarro, Finite Fields
and Their Applications, 50: 84-112, 2018. arXiv version
Conference Proceedings
Success Probability of Decoding Interleaved Alternant Codes
with L. Holzbaur, H. Liu, S. Puchinger, J. Rosenkilde, V. Sidorenko and A. Wachter-Zeh, in 2020 IEEE Information Theory Workshop, 2021.
Invariants and inequivalence of linear rank-metric codes
with S. Puchinger and A.-L. Horlemann-Trautmann, in IEEE International Symposium on Information Theory, pp. 2049-2053, 2019. arXiv version
Book Chapters
Identifying rank-metric codes using Galois group action,
in the Oberwolfach Report of the conference Contemporary Coding Theory (ID 1912), 2019.
Fuzzy Authentication using Rank Distance, with J. Rosenthal and D.
Schipani, In International Worskhop on Communication Security, Lecture
Notes in Electrical Engineering, Springer, 97-108, 2017. arXiv version
Preprints
A proof of the Etzion-Silberstein conjecture for monotone and MDS-constructible Ferrers diagrams, with M. Stanojkovski, arXiv preprint, arXiv:2306.16407, 2023.
Strong blocking sets and minimal codes from expander graphs, with N. Alon, A. Bishnoi and S. Das, arXiv preprint, arXiv:2305.15297, 2023.
Maximum Flag-Rank Distance Codes, with G. N. Alfarano and F. Zullo, arXiv preprint, arXiv:2303.16653, 2023.
Higher-degree symmetric rank-metric codes, with A. Bik, arXiv preprint, arXiv:2303.06745, 2023.
Outer Strong blocking sets, with G. N. Alfarano and M. Borello, arXiv preprint, arXiv:2301.09590, 2023.
Exceptional scattered sequences, with D. Bartoli, G. Marino and L. Vicino, arXiv preprint, arXiv:2211.11477, 2022.
Valued rank-metric codes, with Y. El Maazouz, M. A. Hahn and M. Stanojkovski, arXiv preprint, arXiv:2104.03216, 2021.
Presentations
Invited Talks
SIAM Conference on Applied Algebraic Geometry - Network Coding and Codes in the Rank and Subspace Metrics, Eindhoven (the Netherlands), July 2023.
A Proof of the Etzion-Silberstein Conjecture for Monotone and MDS-Constructible Ferrers Diagrams
NCM29 29th Nordic Congress of Mathematicians (with EMS) -- Algebraic Coding Theory and Cryptography, Aalborg University, Denmark, July 2023
A graph-theoretic construction of minimal linear codes
University of Campania L. Vanvitelli (Italy), May 2023.
Rank-Metric Codes with High Degree of Symmetry
University of Naples Federico II (Italy), May 2023.
Generalizing symmetric rank-metric codes to higher degrees.
University of Trento (Italy), Math Bitse Seminar, March 2023.
Rank-Metric Codes: Theory and Applications
University of Zurich (Switzerland), December 2022.
Asymptotically good minimal linear codes from Ramanujan graphs
Universit Paris 8 (France), S minaire Math matiques Discr tes, Codes et Cryptographie, December 2022.
Explicit constructions of asymptotically good minimal linear codes from Ramanujan graphs
Colloquium on Combinatorial Designs, online, September 2022. One-weight codes in various metrics
ACA 2022 - Applications of Computer Algebra -- q-Analogues in Combinatorics: Matroids, Designs and Codes, Istanbul-Gebze (Turkey), August 2022.
A Geometric Characterization of Near MRD Codes
Leipzig - Magdeburg Seminar Day, Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany), August 2022.
Linear Sperner families and strong blocking sets in coding theory
Algebraic Methods in Coding Theory and Communication -- Casa Matem tica Oaxaca (CMO) (Mexico), April 2022.
Geometric approaches to linear codes.
Video
Sabanci University, Sabanci Algebra Seminar, March 2022.
The Geometry of One-Weight Codes
Seminari UMI Crittografia e Codici -- De Cifris (Italy), October 2021. Matrici Parziali e Polinomi non Commutativi nella Teoria dei Codici.
Video
Universit Paris 8 (France), S minaire Math matiques Discr tes, Codes et Cryptographie, Semptember 2021.
Matrix Algebras, Skew Polynomials and Sum-Rank-Metric Codes
Skolkovo Institute of Science and Technology, Moscow, Skoltech Coding Theory eSeminar, February 2021.
Multivariate Polynomials over Finite Grids and their Applications to Algebraic Coding Theory
University of Kentucky (USA), Algebra eSeminar, September 2020. Spaces of matrices with high rank using Galois theory
Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany), Seminar on Nonlinear Algebra, September 2020.
Linear algebra and Galois theory: Alon-F redi theorem for endomorphisms
Universit degli Studi della Campania "Luigi Vanvitelli" (Italy), eSeminar, July 2020.
Defining Reed--Muller codes in the rank metric: the Alon--F redi theorem for endomorphisms
Inria Saclay Ile-de-France (France), December 2019.
3-Tensors: a natural way of representing rank-metric codes
Universit Paris 8 (France), S minaire Math matiques Discr tes, Codes et Cryptographie, November 2019.
Matrices, tensors and rank-metric codes
Technische Universit t M nchen (Germany), July 2019.
Rank-metric codes and 3-tensors
SIAM Conference on Applied Algebraic Geometry - Network Coding and Subspace Designs, Bern (Switzerland), July 2019.
Invariants of rank-metric codes via Galois group action
Universidad de Alicante (Spain), June 2019.
Representations of Rank-Metric and Gabidulin Codes
Contermporary Coding Theory - Oberwolfach Workshop 1912 (Germany), March 2019.
Identifying rank-metric codes using Galois group action
Algebraic Coding Theory for Networks, Storage, and Security - Dagstuhl Seminar 18511 (Germany), December 2018.
Parametrizing Systematic Gabidulin Codes and Applications
Technische Universit t M nchen (Germany), November 2018.
Encoding schemes for Gabidulin codes with applications
University College Dublin (Ireland), ANT Seminar, October 2018.
Properties of rank metric codes and analogies with the Hamming metric
Universit di Trento (Italy), Seminari UniTN, June 2018.
The Systematic Encoder for Generalized Gabidulin Codes
Universit Paris 8 (France), S minaire Protection de l Information, April 2018.
Analogies between Rank-Metric and Hamming Codes: Old and New
Results
Aalto University, Helsinki (Finland), ANTA Seminar, November 2016.
On the Genericity of Maximum Rank Distance and Gabidulin Codes
Other Talks and Seminars
Fq15, Paris (France), July 2023.
A proof of the Etzion-Silberstein conjecture for strictly monotone Ferrers diagrams
Dutch-Belgian Discrete Math Seminar -- Ghent University (Belgium), January 2023.
Small strong blocking sets via Ramanujan graphs
Irsee -- Finite Geometries 2022 (Germany), August 2022.
Asymptotically good strong blocking sets
Combinatorics 2022, Mantova (Italy), June 2022.
Strong Blocking Sets and Minimal Codes from Graphs
Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany), Seminar on Nonlinear Algebra, June 2021.
Matrices with Restricted Entries, Skew Polynomials and Coding Theory
PhD defense - University of Zurich (Switzerland), July 2019.
Algebraic Theory of Rank-Metric Codes: Representations, Invariants and Density Results
Zurich Graduate Colloquim - University of Zurich (Switzerland), May 2019.
What is... the MDS conjecture?
The Second Colombian Workshop on Coding Theory, Barranquilla (Colombia), January 2019.
On the Cauchy-like structure of generator matrices
for Gabidulin codes
CIMPA Research School and Workshop: Quasi-Cyclic and Related
Algebraic Codes, METU (Turkey), August 2018.
Rank Metric vs. Hamming Metric: Evaluation Codes and their Encoders
Latin American Week on Coding and Information, Unicamp, Campinas (Brazil), July 2018.
Generalized Gabidulin Codes and their Generator Matrices (poster)
Combinatorics 2018, Arco (Italy), June 2018.
Maximum Weight Spectrum Codes
Munich Workshop on Coding and Cryptography 2018 (Germany), April 2018.
The Generator Matrix in Standard Form of Gabidulin Codes (poster)
University of Neuchatel (Switzerland), November 2017.
MRD codes: further properties and standard form of Gabidulin codes
Fq13, Gaeta (Italy), June 2017.
On linear Generalized Twisted Gabidulin codes and the existence of new MRD codes
2nd Workshop on Communication Security, Paris (France), April 2017.
Fuzzy Authentication using Rank Distance
University of Neuchatel (Switzerland), September 2016.
On the Genericity of Maximum Rank Distance and Gabidulin Codes
University of Zurich (Switzerland), November 2015.
On Codes over Skew Polynomial Rings
7th Workshop on Coding and Systems, University of Salamanca (Spain), July 2015.
A new approach for List Decoding of BCH and Reed-Solomon Codes
