Research

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:

• Generalised Evasive Subspaces (old title: Generalized Scattered Subspaces), with A. Gruica, A. Ravagnani and J. Sheekey-> arxiv 

• Waring identifiable subspaces over finite fields, with M. Lavrauw -> arxiv 

• Clubs and their applications, with V. Napolitano, O. Polverino and P. Santonastaso -> arxiv  

• Maximum weight codewords of a linear rank metric code, with O. Polverino and P. Santonastaso -> arxiv 

• On the stabilizer of the graph of linear functions over finite fields, with V. Smaldore and C. Zanella -> arxiv

• New scattered quadrinomials, with V. Smaldore and C. Zanella -> arxiv 

ACCEPTED FOR PUBLICATION:

• On subspace designs, with P. Santonastaso, EMS Surveys in Mathematical Sciences -> arxiv  ->EMSSurvey 

• Maximum flag-rank distance codes, with G. Alfarano and A. Neri, Journal Combinatorial Theory, Series A -> arxiv 

• Saturating linear sets in PG(2,q^4) , Finite Fields and Their Applications -> arxiv 

PUBLICATIONS:

2024

• Geometric dual and sum-rank minimal codes, with M. Borello, Journal of Combinatorial Designs  -> 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

EXTENDED ABSTRACTS/CONFERENCE PAPERS: 

• Fqn-linear rank distance codes and their distinguishers, with L. Giuzzi, WCC 2019 -> arxiv

• 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 

• 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 one-orbit cyclic subspace codes in Gq(n,3), with C. Castello and O. Polverino, ISIT 2024 -> arxiv 

• Two-weight rank-metric codes, with O. Polverino, P. Santonastaso and J. Sheekey ISIT 2024 -> arxiv