RESEARCH INTERESTS: Finite geometries and coding theory
Finite Fields
Rank metric codes
Incidence structures
Linear codes
Blocking sets
Linear sets
Decoding
Polynomials over finite fields
PREPRINTS:
Representability of the direct sum of uniform q-matroids, with G. Alfarano, R. Jurrius and A. Neri -> arxiv
The geometry of codes for Random Access in DNA storage, with A. Gruica and M. Montanucci -> arxiv
Quasi-optimal cyclic orbit codes, with C. Castello, H. Gluesing-Luerssen and O. Polverino -> arxiv
Invariants for sum-rank metric codes, with P. Santonastaso -> arxiv
ACCEPTED FOR PUBLICATION:
On the stabilizer of the graph of linear functions over finite fields, with V. Smaldore and C. Zanella, Forum Mathematicum -> arxiv -> FM
Using multi-orbit cyclic subspace codes for constructing optical orthogonal codes, with F. Ozbudak and P. Santonastaso, Cryptography and Communications -> arxiv
On perfect symmetric rank-metric codes, with Usman Musharraf, Archiv der Mathematik -> arxiv
Whitney numbers of rank-metric lattices and code enumeration, with G. Cotardo and A. Ravagnani, Advances in Applied Mathematics -> arxiv
PUBLICATIONS:
2025
Waring identifiable subspaces over finite fields, with M. Lavrauw, Journal of Algebraic Combinatorics 61(2) (2025) -> arxiv -> JACO
Full weight spectrum one-orbit cyclic subspace codes, with C. Castello and O. Polverino, Journal Combinatorial Theory, Series A 212 (2025), 106005 -> arxiv -> JCTA
2024
Geometric dual and sum-rank minimal codes, with M. Borello, Journal of Combinatorial Designs -> arxiv -> JCD
Maximum flag-rank distance codes, with G. Alfarano and A. Neri, Journal Combinatorial Theory, Series A 207 (2024), 105908 -> arxiv -> JCTA
Saturating linear sets in PG(2,q^4) , Finite Fields and Their Applications 97 (2024), 102447 -> arxiv -> FFA
On subspace designs, with P. Santonastaso, EMS Surveys in Mathematical Sciences 11(1) (2024), 1-62 -> arxiv ->EMSSurvey
Clubs and their applications, with V. Napolitano, O. Polverino and P. Santonastaso, SIAM Journal on Applied Algebra and Geometry 8(3) (2024), 493-518 -> arxiv -> SIAGA
New scattered quadrinomials, with V. Smaldore and C. Zanella, Linear Algebra and its Applications 702 (2024), 143-160 -> arxiv -> LAA
Maximum weight codewords of a linear rank metric code, with O. Polverino and P. Santonastaso, SIAM Journal on Discrete Mathematics 38(4) (2024), 2665-2690 -> arxiv -> SIDMA
Generalised Evasive Subspaces (old title: Generalized Scattered Subspaces), with A. Gruica, A. Ravagnani and J. Sheekey, Journal of Combinatorial Designs 32(11) (2024), 642-678-> arxiv -> JCD
2023
The geometry of one-weight codes in the sum-rank metric, with A. Neri and P. Santonastaso, Journal of Combinatorial Theory, Series A 194 (2023), 105703 -> arxiv -> JCTA
Two pointsets in PG(2,qn) and the associated codes -> with V. Napolitano, O. Polverino and P. Santonastaso, Advances in Mathematics of Communications 17(1) (2023), 227-245 -> arxiv -> AMC
Multi-orbit cyclic subspace codes and linear sets (old title: Multi-Sidon spaces over finite fields), Finite Fields and Their Applications 87 (2023), 102153 -> arxiv -> FFA
On the automorphism groups of Lunardon-Polverino scattered linear sets, with W. Tang and Y. Zhou, Discrete Mathematics 346(5) (2023), 113313-> arxiv -> DM
Codes with few weights arising from linear sets, with V. Napolitano, Advances in Mathematics of Communications 17(2) (2023) -> arxiv ->AMC
Rank-metric codes, semifields, and the avarage critical problem, with A. Gruica, A. Ravagnani and J. Sheekey, SIAM Journal on Discrete Mathematics 37(2) (2023)-> arxiv -> SIDMA
Linear maximum rank distance codes of exceptional type, with D. Bartoli and G. Zini, IEEE Transactions on Information Theory 69(6) (2023) -> arxiv -> IEEE
Divisible linear rank metric codes, with O. Polverino, P. Santonastaso and J. Sheekey, IEEE Transactions on Information Theory 69(7) (2023)-> arxiv -> IEEE
Cones from maximum h-scattered linear sets and a stability result for cylinders from hyperovals, with S. Adriaensen, J. Mannaert and P. Santonastaso, Discrete Mathematics 346(12) (2023) -> arxiv -> DM
Classifications and constructions of minimum size linear sets, with V. Napolitano, O. Polverino and P. Santonastaso, Finite Fields and Their Applications 92 (2023), 102280 -> arxiv -> FFA
Constructions and equivalence of Sidon spaces, with C. Castello, O. Polverino and P. Santonastaso, Journal of Algebraic Combinatorics 54 (2023) -> arxiv -> JACO
2022
Investigating the exceptionality of scattered polynomials, with D. Bartoli and G. Zini, Finite Fields and Their Applications 77 (2022), 101956-> arxiv -> FFA
Linearized trinomials with maximum kernel, with P. Santonastaso, Journal of Pure and Applied Algebra 226(3) (2022), 106842 -> arxiv ->JPAA
On the infiniteness of a family of APN functions, with D. Bartoli, M. Calderini and O. Polverino, Journal of Algebra 598 (2022), 68-84 -> arxiv -> JAlgebra
r-fat linearized polynomials over finite fields, with D. Bartoli, G. Micheli and G. Zini, Journal of Combinatorial Theory, Series A, 189 (2022), 105609 -> arxiv -> JCTA
Linear sets on the projective line with complementary weights, with V. Napolitano, O. Polverino and P. Santonastaso, Discrete Mathematics 345(7) (2022), 112890 -> arxiv -> DM
Extending two families of maximum rank distance codes, with A. Neri and P. Santonastaso, Finite Fields and Their Applications 81 (2022), 102045 -> arxiv -> FFA
Non-minimum tensor rank Gabidulin codes, with D. Bartoli and G. Zini, Linear Algebra and its Applications 650 (2022), 248-266 -> arxiv -> LAA
On the list decodability of rank-metric codes containing Gabidulin codes, with P. Santonastaso, Designs, Codes and Cryptography 90 (2022), 957-982 -> arxiv ->DESI
Encoding and decoding of several optimal rank metric codes, with W.K. Kadir and C. Li, Cryptography and Communications 14 (2022), 1281-1300 -> arxiv -> CC
2021
Scattered subspaces and related codes, with G. Zini, Designs, Codes and Cryptography 89 (2021), 1853-1873 -> arxiv -> DESI
On the intersection problem for linear sets in the projective line, with G. Zini, Discrete Mathematics 344(6) (2021), 112359 -> arxiv -> DM
Generalising the scattered property of subspaces, with B. Csajbók, G. Marino and O. Polverino, Combinatorica 41 (2021), 237-262 -> arxiv -> CCC
On certain linearized polynomials with high degree and kernel of small dimension, with O. Polverino and G. Zini, Journal of Pure and Applied Algebra 225(2) (2021) -> arxiv -> JPAA
Linear sets from projection of Desarguesian spreads, with V. Napolitano, O. Polverino and G. Zini, Finite Fields and Their Applications 71 (2021), 1-19 ->arxiv -> FFA
On maximum additive Hermitian rank-metric codes, with R. Trombetti, Journal of Algebraic Combinatorics 54 (2021), 151-171 ->arxiv ->JACO
2020
A new family of maximum scattered linear sets in PG(1,q6), with D. Bartoli and C. Zanella, Ars Mathematica Contemporanea 19(1) (2020), 125-145 -> arxiv -> AMC
Connections between scattered linear sets and MRD-codes, with O. Polverino, Bulletin of the Institute of Combinatorics and its Applications 89 (2020)-> arxiv -> BICA
On the number of roots of some linearized polynomials, with O. Polverino, Linear Algebra and its Applications 601 (2020), 189-218 -> arxiv ->LAA
On the list decodability of Rank Metric codes, with R. Trombetti, IEEE Transactions on Information Theory 66(9) (2020), 5379-5386 -> arxiv ->IEEE
Vertex properties of maximum scattered linear sets of PG(1,qn), with C. Zanella, Discrete Mathematics 343 (5) (2020) -> arxiv ->DM
MRD-codes arising from the trinomial xq+xq3+cxq5∈Fq6[x] , with G. Marino and M. Montanucci, Linear Algebra and its Applications 591 (2020), 99-114 -> arxiv ->LAA
2019
Identifiers for MRD-codes, with L. Giuzzi, Linear Algebra and its Applications 575 (2019), 66-86 -> arxiv -> LAA
A characterization of linearized polynomials with maximum kernel, with B. Csajbók, G. Marino and O. Polverino, Finite Fields and Their Applications, 56 (2019), 109-130 -> arxiv -> FFA
2018
New maximum scattered linear sets of the projective line, with B. Csajbók and G. Marino, Finite Fields and Their Applications 54, (2018), 133-150 ->arxiv ->FFA
Codes arising from incidence matrices of points and hyperplanes in PG(n, q), with O. Polverino, Journal of Combinatorial Theory, Series A 158 (2018), 1-11 ->arxiv ->JCTA
2017
Maximum scattered linear sets and MRD-codes, with B. Csajbók, G. Marino and O. Polverino, Journal of Algebraic Combinatorics (2017): 1-15 -> JACO
BOOKS:
Chapter Geometrie di Galois e Codici Lineari, in 100 TESI DI CRITTOGRAFIA E CODICI IN ITALIA 2008-2017 (D. Bartoli, N. Murru, F. Pavese and M. Sala), Aracne, Crittografia 3 ->Aracne
Rappresentazioni di gruppi-un'introduzione, with A. Russo, Aracne, Algoritmica 4 (2017) ->Aracne
CONFERENCE PAPERS:
On interpolation-based decoding of a class of maximum rank distance codes, with W.K. Kadir and C. Li, ISIT 2021 ->arxiv
Hermitian rank-metric codes, with R. Trombetti, EUROCOMB 2021 -> EUROCOMB2021
On one-orbit cyclic subspace codes in Gq(n,3), with C. Castello and O. Polverino, ISIT 2024 -> arxiv -> IEEE
Two-weight rank-metric codes, with O. Polverino, P. Santonastaso and J. Sheekey ISIT 2024 -> arxiv -> IEEE
On r-fat polynomials, with O. Polverino and P. Santonastaso, WAIFI 2024
Identifying glyphs in rock engravings using statistical information, with S. Crisci, V. De Simone and A. Diana accepted for publication CEUR Workshop Proceedings Amalart 2024
A nonnegative matrix factorization-based data augmentation procedure for two-dimensional data, with S. Crisci and V. De Simone accepted for publication CEUR Workshop Proceedings Amalart 2024
EXTENDED ABSTRACTS:
Fqn-linear rank distance codes and their distinguishers, with L. Giuzzi, WCC 2019 -> arxiv
Decoding a class of maximum Hermitian rank metric codes, with W.K. Kadir and C. Li, BFA 2021 -> arxiv
On a family of MRD codes with parameters [nxn,2n,n-1]q, n even, with O. Polverino, M. Timpanella and G. Zini -> WCC2022
Algebraic and Geometrical aspects of cyclic subspace codes -> MTNS 2022
Left ideali LRPC codes and a ROLLO-type cryptosystem based on group algebras, with M. Borello and P. Santonastaso, ALCOCRYPT conference -> arxiv
On the maximum weight codewords of linear rank-metric codes, with O. Polverino and P. Santonastaso, WCC2024
Stabilizers of graphs of linear functions and rank-metric codes, with V. Smaldore and C. Zanella, WCC2024