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Alessandro Neri's Home Page

About me

I am currently a postdoctoral researcher in the Nonlinear Algebra Group at the Max Planck Institute for Mathematics in the Sciences, in Leipzig. 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, Daniel Augot, Jessica Bariffi, Tristram Bogart, Martino Borello, Eimear Byrne, Alain Couvreur, Yassine El Maazouz, José Gómez Torrecillas, Marvin Anas Hahn, Lukas Holzbaur, Anna-Lena Horlemann-Trautmann, Julien Lavauzelle, Hedongliang Liu, Fco. Javier Lobillo Borrero, David Karpuk, Sam Mattheus, Giacomo Micheli, Diego Napp, Gabriel Navarro, Sven Puchinger, Tovohery Hajatiana Randrianarisoa, Alberto Ravagnani, Julian Renner, Veronica Requena, Johan Rosenkilde, Joachim Rosenthal, Davide Schipani, John Sheekey, Minjia Shi, Vladimir Sidorenko, Patrick Solé, Mima Stanojkovski, Mauricio Velasco, Antonia Wachter-Zeh. Ferdinando Zullo.


Co-organizer of the session Algebraic and Geometric Methods in Coding Theory for the conference ACA 2022 - Applications of Computer Algebra, 15-19 August 2022, Istanbul-Gebze, Turkey.

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 to the conference Finite Geometries: Sixth Irsee Conference, 28 August - 3 September 2022, Irsee, Germany.

Invited speaker for the Seminars on Cryptography and Coding Theory organized by Unione Matematica Italiana. Here the video of the talk (in Italian).


Email address alessandro.neri[at]
Office room F3 13, Max Planck Institute for Mathematics in the Sciences
Phone +49 (0) 341 - 9959 - 781
Postal address Inselstrasse 22, 04103 Leipzig

Research Activity


Jounal Publications

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. Solé, 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. Solé, 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. Gómez-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


Evasive subspaces, generalized rank weights and near MRD codes, with G. Marino and R. Trombetti, arXiv preprint, arXiv:2204.11791, 2022.

The geometry of one-weight codes in the sum-rank metric, with P. Santonastaso and F. Zullo, arXiv preprint, arXiv:2112.04989, 2021.

Linear Cutting Blocking Sets and Minimal Codes in the Rank Metric, with G. N. Alfarano, M. Borello and A. Ravagnani, arXiv preprint, arXiv:2106.12465, 2021.

Twisted Linearized Reed-Solomon Codes: A Skew Polynomial Framework, arXiv preprint, arXiv:2105.10451, 2021.

Valued rank-metric codes, with Y. El Maazouz, M. A. Hahn and M. Stanojkovski, arXiv preprint, arXiv:2104.03216, 2021.

Moderate Density Parity-Check Codes from Projective Bundles, with J. Bariffi, S. Mattheus and J. Rosenthal, arXiv preprint, arXiv:2103.09722, 2021.

Weighted Reed-Solomon convolutional codes, with G. N. Alfarano, D. Napp and V. Requena, arXiv preprint, arXiv:2012.11417, 2020.


Invited Talks

Algebraic Methods in Coding Theory and Communication -- Casa Matemática Oaxaca (CMO) (Mexico), April 2022.
Geometric approaches to linear codes.

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.

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-Füredi theorem for endomorphisms

Universitŕ degli Studi della Campania "Luigi Vanvitelli" (Italy), eSeminar, July 2020.
Defining Reed--Muller codes in the rank metric: the Alon--Füredi theorem for endomorphisms

Inria Saclay Ile-de-France (France), December 2019.
3-Tensors: a natural way of representing rank-metric codes

Université Paris 8 (France), Séminaire Mathématiques Discrčtes, Codes et Cryptographie, November 2019.
Matrices, tensors and rank-metric codes

Technische Universität München (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 Universität München (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

Universitá di Trento (Italy), Seminari UniTN, June 2018.
The Systematic Encoder for Generalized Gabidulin Codes

Université Paris 8 (France), Séminaire 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

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