Recent publications

This is the list of the papers coauthored by at least one of the member of our research group since 2012.

PREPRINTS:

• Generalized Evasive Subspaces, A. Gruica, A. Ravagnani, J. Sheekey and F. Zullo -> arxiv 

• Waring identifiable subspaces over finite fields, M. Lavrauw and F. Zullo -> arxiv 

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

• On the minimum size of linear sets, S. Adriaensen and P. Santonastaso -> arxiv 

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

• Geometric dual and sum-rank minimal codes, M. Borello and F. Zullo-> arxiv 

• Maximum flag-rank distance codes, G. Alfarano, A. Neri and F. Zullo -> arxiv 

• On MSRD codes, h-designs and disjoint maximum scattered linear sets, J. Sheekey and P. Santonastaso -> arxiv

ACCEPTED FOR PUBLICATION:

• On subspace designs, P. Santonastaso and F. Zullo, EMS Surveys in Mathematical Sciences -> arxiv  

• Constructions and equivalence of Sidon spaces, with C. Castello, O. Polverino and P. Santonastaso, Journal of Algebraic Combinatorics -> arxiv 

PUBLICATIONS:

2023

• The geometry of one-weight codes in the sum-rank metric, A. Neri, P. Santonastaso and F. Zullo,  Journal of Combinatorial Theory, Series A 194 (2023), 105703 -> arxiv -> JCTA 

• Two pointsets in PG(2,qn) and the associated codes, V. Napolitano, O. Polverino, P. Santonastaso and F. Zullo, 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), F. Zullo, Finite Fields and Their Applications 87 (2023), 102153  -> arxiv  -> FFA 

• On the automorphism groups of Lunardon-Polverino scattered linear sets, W. Tang, Y. Zhou and F. Zullo, Discrete Mathematics 346(5) (2023)-> arxiv ->DM 

• Codes with few weights arising from linear sets, V. Napolitano and F. Zullo, Advances in Mathematics of Communications 17(2) (2023), 320-332 -> arxiv ->AMC 

• Rank-metric codes, semifields, and the avarage critical problem, A. Gruica, A. Ravagnani, J. Sheekey and F. Zullo, SIAM Journal on Discrete Mathematics 37(2) (2023)-> arxiv  -> SIDMA 

• Linear maximum rank distance codes of exceptional type, D. Bartoli, G. Zini and F. Zullo, IEEE Transactions on Information Theory 69(6) (2023) -> arxiv -> IEEE

• Divisible linear rank metric codes, O. Polverino, P. Santonastaso,  J. Sheekey and F. Zullo, 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, S. Adriaensen, J. Mannaert, P. Santonastaso  and F. Zullo, Discrete Mathematics 346(12) (2023) -> arxiv -> DM 

• A new combinatorial characterization of (quasi)-Hermitian sufaces, V. Napolitano, Journal of Geometry 114(2) (2023) -> JG 

• Classifications and constructions of minimum size linear sets, V. Napolitano, O. Polverino, P. Santonastaso and F. Zullo, Finite Fields and Their Applications 92 (2023), 102280 -> arxiv -> FFA 

2022

• Investigating the exceptionality of scattered polynomials, D. Bartoli, G. Zini and F. Zullo, Finite Fields and Their Applications  77 (2022), 101956-> arxiv -> FFA 

• Linearized trinomials with maximum kernel, P. Santonastaso and F. Zullo, Journal of Pure and Applied Algebra 226(3) (2022), 106842 -> arxiv   ->JPAA 

• On the infiniteness of a family of APN functions, D. Bartoli, M. Calderini, O. Polverino and F. Zullo, Journal of Algebra 598 (2022), 68-84 -> arxiv -> JAlgebra 

• r-fat linearized polynomials over finite fields, D. Bartoli, G. Micheli, G. Zini and F. Zullo, Journal of Combinatorial Theory, Series A, 189 (2022), 105609 -> arxiv -> JCTA 

• Linear sets on the projective line with complementary weights, V. Napolitano, O. Polverino, P. Santonastaso and F. Zullo, Discrete Mathematics 345(7) (2022), 112890 -> arxiv -> DM 

• Extending two families of maximum rank distance codes, A. Neri, P. Santonastaso and F. Zullo, Finite Fields and Their Applications 81 (2022), 102045 -> arxiv -> FFA 

• Non-minimum tensor rank Gabidulin codes, D. Bartoli, G. Zini and F. Zullo, Linear Algebra and its Applications 650 (2022), 248-266 -> arxiv       -> LAA 

• On the list decodability of rank-metric codes containing Gabidulin codes, P. Santonastaso and F. Zullo, Designs, Codes and Cryptography 90 (2022), 957-982 -> arxiv ->DESI 

• Encoding and decoding of several optimal rank metric codes, W.K. Kadir, C. Li and F. Zullo, Cryptography and Communications 14 (2022), 1281-1300 -> arxiv -> CC 

• Note on sets of hyperplane-type (m,n)r-1 in PG(r,q), Australasian Journal of Combinatorics 82(2) (2022), 197-200 -> AJC 

• On (q^2+q+1)-sets of plane-type (m,n,r)2 in PG(3,q), International Eletronic Journal of Geometry 15 (2022), 79-82 -> IEJG 

2021

• Scattered subspaces and related codes, G. Zini and F. Zullo, Designs, Codes and Cryptography 89 (2021), 1853-1873 -> arxiv -> DESI 

• On the intersection problem for linear sets in the projective line, G. Zini and F. Zullo, Discrete Mathematics 344(6) (2021), 112359  -> arxiv        -> DM 

• Generalising the scattered property of subspaces, B. Csajbók, G. Marino, O. Polverino and F. Zullo, Combinatorica 41 (2021), 237-262 -> arxiv  -> CCC 

• On certain linearized polynomials with high degree and kernel of small dimension, O. Polverino, G. Zini and F. Zullo, Journal of Pure and Applied Algebra 225(2) (2021) -> arxiv -> JPAA 

• Linear sets from projection of Desarguesian spreads, with V. Napolitano, O. Polverino, G. Zini and F. Zullo, Finite Fields and Their Applications 71 (2021),  1-19 ->arxiv -> FFA 

• On maximum additive Hermitian rank-metric codes, R. Trombetti and F. Zullo, Journal of Algebraic Combinatorics 54 (2021), 151-171 ->arxiv    ->JACO 

• Small stopping sets in finite projective planes of order q, V. Napolitano, Art of Discrete and Applied Mathematics 4(3) (2021) -> ArtDAM 

• On Baer cones in PG(3,q), V. Napolitano, Journal of Geometry 112(3) (2021), 37 -> JG 

2020

• A new family of  maximum scattered linear sets in PG(1,q6), D. Bartoli, C. Zanella and F. Zullo, Ars Mathematica Contemporanea 19(1) (2020), 125-145 -> arxiv -> AMC 

• Connections between scattered linear sets and MRD-codes, O. Polverino and F. Zullo,  Bulletin of the Institute of Combinatorics and its Applications 89 (2020)-> arxiv -> BICA

• On the number of roots of some linearized polynomials, O. Polverino and F. Zullo, Linear Algebra and its Applications 601 (2020), 189-218 -> arxiv ->LAA

• On the list decodability of Rank Metric codes, R. Trombetti and F. Zullo,  IEEE Transactions on Information Theory 66(9) (2020), 5379-5386 -> arxiv ->IEEE

• Vertex properties of maximum scattered linear sets of PG(1,qn), C. Zanella and F. Zullo, Discrete Mathematics 343 (5) (2020) -> arxiv ->DM

• MRD-codes arising from the trinomial xq+xq3+cxq5∈Fq6[x] , G. Marino, M. Montanucci and F. Zullo, Linear Algebra and its Applications 591 (2020), 99-114 -> arxiv ->LAA

• MRD codes with maximum idealisers, B. Csajbók, G. Marino, O. Polverino and Y. Zhou,  Discrete Mathematics 343(9) (2020) -> arxiv -> DM 

• Cones in PG(3,q), V. Napolitano, Note di Matematica 40(1) (2020), 81-86 -> NM 

• On sets of plane-type (0,mq,2mq)2 in PG(3,q) with a long secant, V. Napolitano, Journal of Geometry 111(3) (2020), 50 -> JG 

2019

• Identifiers for MRD-codes, L. Giuzzi and F. Zullo, Linear Algebra and its Applications 575 (2019), 66-86  -> arxiv -> LAA

• A characterization of linearized polynomials with maximum kernel, B. Csajbók, G. Marino, O. Polverino and F. Zullo, Finite Fields and Their Applications, 56 (2019), 109-130  -> arxiv -> FFA

• A Carlitz type result for linearized polynomials, B. Csajbók, G. Marino and O. Polverino,  Ars Mathematica Contemporanea 16(2) (2019), 585-608 -> arxiv -> AMC 

• Two characterization of the family of secant lines of an ovoid of PG(3,q), V. Napolitano, Journal of Geometry 110(2) (2019), 21 -> JG 

2018

• New maximum scattered linear sets of the projective line, B. Csajbók, G. Marino and F. Zullo,  Finite Fields and Their Applications 54,  (2018), 133-150 -> arxiv ->FFA

• Codes arising from incidence matrices of points and hyperplanes in PG(n, q), O. Polverino and F. Zullo, Journal of Combinatorial Theory, Series A  158 (2018),  1-11  ->arxiv ->JCTA

• A new family of MRD-codes, B. Csajbók, G. Marino, O. Polverino and C. Zanella, Linear Algebra and its Applications 548 (2018), 203-220 -> arxiv  -> LAA 

• Classes and equivalence of linear sets in PG(1,q^n), B. Csajbók, G. Marino and O. Polverino, Journal of Combinatorial Theory, Series A 157 (2018), 402-426 -> arxiv  -> JCTA 

• Maximum scattered linear sets and complete caps in Galois spaces, D. Bartoli, M. Giulietti, G. Marino and O. Polverino, Combinatorica 38(2) (2018), 255-278 -> arxiv -> CCC 

• A new characteriation of elliptic quadrics in PG(3,q), q odd, V. Napolitano, AAPP Atti della Accademia Peloritana dei Pericolanti, Classe di Scienze Fisiche, Matematiche e Naturali 96 (2018), A101-A104 -> AAPP 

2017

• Maximum scattered linear sets and MRD-codes, B. Csajbók, G. Marino, O. Polverino and F. Zullo, Journal of Algebraic Combinatorics (2017): 1-15 -> JACO

• On almost small and almost large super-Vandermonde sets in GF(q), A. Blokhuis, G. Marino, F. Mazzocca and O. Polverino, Designs, Codes and Cryptography 84(1-2), (2017), 197-201 -> DESI 

• The generalized translation dual of finite semifields, G. Lunardon, G. Marino, O. Polverino and R. Trombetti, Annals of Combinatorics 21(4) 

(2017), 629-643 -> AC 

• Note: An inequality for line-size sum in a finite linear space, V. Napolitano, Australasian Journal of Combinatorics 68(1) (2017), 118-121 -> AJC 

• An easy characterization of PG(4,n), V. Napolitano and D. Olanda, Journal of Geometry 108(2) (2017), 375-381-> JG 

• Ruled sets of plane-type (m,h)2 in PG(3,q) with m<=q, V. Napolitano, Journal of Geometry 108(3) (2017), 953-960 -> JG 

2016

• On sets of type (m,h)2 in PG(3,q) with m<= q, V. Napolitano, Note di Matematica 35(1) (2016), 109-123 -> NM

• On quasi-Hermitian varieties in PG(3,q^2), V. Napolitano, Discrete Mathematics 339(2) (2016), 511-514 -> DM 

• Sets of type (q+1,n) in PG(3,q), N. Durante, V. Napolitano and D. Olanda, Journal of Geometry 107(1) (2016), 9-18 -> JG 

• Sets of type (q,n) in PG(3,q), N. Durante, V. Napolitano and D. Olanda, Ricerche di Matematica 65(1) (2016), 65-70 -> RM 

2015

•  Solution to an isotopism question concerning rank 2 semifields, M. Lavrauw, G. Marino, O. Polverino and R. Trombetti, Journal of Combinatorial Designs 23(2) (2015), 60-77 -> arxiv -> JCD 

• The isotopism problem of a class of 6-dimensional rank 2 semifields and its solution, M. Lavrauw, G. Marino, O. Polverino and R. Trombetti, Finite Fields and their Applications 34 (2015), 250-264 -> arxiv  -> FFA 

• On translation spreads of H(q), G. Marino and O. Polverino, Journal of Algebraic Combinatorics 42(3) (2015), 725-744 -> JACO 

• A characterization of the hermitian variety in finite 3-dimensional projective spaces, Electronic Journal of Combinatorics 22(1) (2015) -> EJC 

2014

•  Maximum scattered linear sets of pseudoregulus type and the Segre variety S_{n,n}, G. Lunardon, G. Marino, O. Polverino and R. Trombetti,  Journal of Algebraic Combinatorics 39(4) (2014),  807-831 -> arxiv  -> JACO 

• Subplanes of a translation plane, V. Jha, O. Polverino and R. Trombetti, Finite Fields and their Applications 30 (2014), 121-138 -> FFA 

• Note on a class of (q+1)-sets of PG(3,q), V. Napolitano, Australasian Journal of Combinatorics 59(1) (2014), 157-160 -> AJC 

• A simple new proof of the fundamental theorem for finite linear spaces, V. Napolitano and D. Olanda, Ricerche di Matematica 63(1) (2014), 41-45 -> RM 

• Projective spaces and inverive planes, V. Napolitano and D. Olanda, Ricerche di Matematica 63(1) (2014), 239-247 -> RM 

• On (q^2+q+1)-sets of class [1,m,n]2 in PG(3,q), V. Napolitano, Journal of Geometry 105(3) (2014), 449-455 -> JG 

2013

•  A remark on symplectic semifields planes and Z_4-linear codes, G. Lunardon, G. Marino, O. Polverino and R. Trombetti, Designs, Codes and Cryptography 69 (2013), 143-149 -> DESI 

• On the ubiquity and utility of cyclic schemes, M. Abreu, M.J. Funk, D. Labbate and V. Napolitano, Australasian Journal of Combinatorics 55 (2013), 95-120 -> arxiv -> AJC 

• On (q^2+q+1)-sets of class [1,m,n]2 in PG(3,q), V. Napolitano, Electronic Notes in Discrete Mathematics 40 (2013), 283-287 -> ENDM 

• Finite planar spaces with a spread of short lines, V. Napolitano and D. Olanda, Ricerche di Matematica 62(1) (2013), 107-116 -> RM 

• A common characterization of projective spaces PG(4,n) and PG(5,n), V. Napolitano and D. Olanda, Journal of Geometry 104(3) (2013), 563-569 -> JG 

• On sets of type (q+1,n)2 in finite three-dimensional projective spaces, V. Napolitano, Journal of Geometry 104(3) (2013), 557-562 -> JG 

2012

•  On isotopisms and strong isotopisms of commutative presemifields, G. Marino and O. Polverino, Journal of Algebraic Combinatorics 36(2) (2012),  247-261 -> arxiv  -> JACO 

• On the nuclei of a finite semifield, G. Marino and O. Polverino, in Theory and Applications of Finite Fields, Contemporary Mathematics, vol. 579, Amer. Math. Soc., Providence, RI, 2012, pp. 123-141 -> arxiv 

• Fractional dimension of binary Knuth semifield planes, O. Polverino and R. Trombetti,  Journal of Combinatorial Designs 20(7) (2012),  317-327 -> JCD 

• Invariant adjacency matrices of configuration graphs, M. Abreu, M.J. Funk, D. Labbate and V. Napolitano, Linear Algebra and Its Applications 437(8) (2012), 2026-2037 -> LAA 

• Sets of type (3,h) in PG(3,q), V. Napolitano and D. Olanda, Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni 23(4) (2012), 395-403 -> AttiANL 

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), F. Zullo, Aracne, Crittografia 3 -> Aracne 

• Rappresentazioni di gruppi-un'introduzione, A. Russo and F. Zullo, Aracne, Algoritmica 4 (2017)  -> Aracne

EXTENDED ABSTRACTS/CONFERENCE PAPERS: 

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

• On interpolation-based decoding of a class of maximum rank distance codes, W.K. Kadir, C. Li and F. Zullo, ISIT 2021 -> arxiv 

• Hermitian rank-metric codes, R. Trombetti and F. Zullo, EUROCOMB 2021 -> EUROCOMB2021 

• Decoding a class of maximum Hermitian rank metric codes, W.K. Kadir, C. Li and F. Zullo, BFA 2021 -> arxiv 

• On a family of MRD codes with parameters [nxn,2n,n-1]q, n even, O. Polverino, M. Timpanella, G. Zini and F. Zullo -> WCC2022

• Algebraic and Geometrical aspects of cyclic subspace codes, F. Zullo -> MTNS 2022 

• Left ideali LRPC codes and a ROLLO-type cryptosystem based on group algebras, M. Borello,  P. Santonastaso and F. Zullo, ALCOCRYPT conference   -> arxiv