Maria Montanucci - Research

RESEARCH INTERESTS

Algebraic curves over finite fields and their applications:

My main research interests concern Galois Geometries, their applications to Coding Theory and Cryptography, and their interactions with Algebraic Curves over Finite Fields.

Algebraic function fields of one variable (towers of function fields)
Algebraic Geometry in positive characteristic (automorphisms of curves, maximal curves)
Coding Theory (functional codes, AG codes, quantum codes, convolutional codes)
Linear sets and their applications (scattered polynomials, MRD codes)
Permutation polynomials over finite fields and their applications (bent functions)

JOURNAL PUBLICATIONS

48. P. Beelen, T. Drue, M. Montanucci and G. Zini, Non-isomorphic subfields of the BM and GGS maximal function fields [Accepted for publication. To appear].

47. P. Beelen, M. Montanucci and L. Vicino, Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, q =0 (mod 3), Finite

Fields Appl. (to appear).

46. P. Beelen, M. Montanucci and L. Vicino, Weierstrass semigroups and automorphism group of a maximal function field with the third largest possible genus, q =1 (mod 3), Finite

Fields Appl. 109 (2026), Paper No. 102701, 32 pp.

45. P. Beelen, Peter, M. Montanucci and J. Niemann, On the generalized Suzuki curve, Advances in Geometry, vol. 25, no. 3 (2025) pp. 335-344.

DOI: https://doi.org/10.1515/advgeom-2025-0022

44. P. Beelen, M. Montanucci, J. Niemann and L. Quoos, A family of non-isomorphic maximal function fields, Math. Z. 309 (2025), no. 2, Paper No. 19, 22 pp.

43. P. Beelen and M. Montanucci, List-decoding of AG codes without genus penalty, IEEE Trans. Inform. Theory 71 (2025), no. 2, 871-880.

42. P. Beelen, M. Datta, M. Montanucci and J. Niemann, Intersection of irreducible curves and the Hermitian curve, J. Algebra 671 (2025), 75-94.

41. M. Montanucci, G. Tizziotti and G. Zini, On the automorphism group of a family of maximal curves not covered by the Hermitian curve, Finite Fields Appl. 99, 102498

(2024).

40. M. Montanucci and G. Tizziotti, Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve, Designs Codes and Cryptography 91, pp. 831-851 (2023).

39. P. Beelen, M. Montanucci and L. Vicino,Weierstrass semigroups and automorphism group of a maximal curve with the third largest genus, Finite Fields Appl. 92, 102300 (2023).

38. P. Beelen, L. Landi, M. Montanucci, Classication of all Galois subcovers of the Skabelund maximal curves, J.Number Theory 242, pp. 46-72 (2023).

37. M. Montanucci, On algebraic curves with many automorphisms in characteristic p, Mathematische Zeitschrift 301, pp. 3695-3711 (2022).

36. M. Montanucci and C. Zanella, On maximum scattered linear sets in $PG(1,q^5)$, Finite Fields Appl. 78 101983 (2022) DOI: https://doi.org/10.1016/j.ffa.2021.101983

35. M. Giulietti, M. Kawakita, S. Lia and M. Montanucci, An $\mathbb{F}_{p^2}$-maximal Wiman's sextic and its automorphisms, Adv. Geom. 21 (2021), 451-461.

34. D. Bartoli, M. Montanucci and F. Torres, $\mathbb{F}_{p^2}$-maximal curves with many automorphisms are Galois-covered by the Hermitian curve, Adv. Geom. 21 (2021), 325-336.

33. D. Bartoli, B. Csajbók and M. Montanucci, On a conjecture on maximum scattered linear sets in PG(1,q^6), Linear Algebra and its Appl. 631 (2021), 111-135.

32. D. Bartoli, M. Montanucci and G. Zini, On certain self-orthogonal AG codes with applications to Quantum error-correcting codes, Des. Codes Cryptogr. 89 (2021), 1221-1239.

31. P. Beelen, L. Landi and M. Montanucci, Weierstrass semigroups on the Skabelund maximal curve, Finite Fields Appl. 72 101811 (2021) DOI: https://doi.org/10.1016/j.ffa.2021.101811.

30. D. Bartoli and M. Montanucci, On the classification of exceptional scattered polynomials, Journal of Combinatorial Theory Series A 179 105386 (2021) DOI: https://doi.org/10.1016/j.jcta.2020.105386.

29. D. Bartoli, M. Montanucci and G. Zini, Weierstrass semigroups at every point of the Suzuki curve, Acta Arithmetica 197 (2021), 1-20.

28. D. Bartoli, M. Giulietti, M. Kawakita and M. Montanucci, New examples of maximal curves with low genus, Finite Fields and Appl. 68 101744 (2020) DOI: https://doi.org/10.1016/j.ffa.2020.101744.

27. P. Beelen and M. Montanucci, On subfields of the second generalization of the GK maximal function field, Finite Fields Appl. 64 101669 (2020) DOI: https://doi.org/10.1016/j.ffa.2020.101669.

26. M. Montanucci and V. Pallozzi Lavorante, AG codes from the second generalization of the GK maximal curve, Discrete Math. 343 111810 (2020) DOI: https://doi.org/10.1016/j.disc.2020.111810.

25. D. Bartoli, M. Montanucci and L. Quoos, Locally recoverable codes from automorphism groups of function fields of genus $g \geq 1$, IEEE Transactions on Information Theory 66 (2020), 6799-6808.

24. M. Montanucci and G. Zini, Quotients of the Hermitian curve from subgroups of PGU(3,q) without fixed points or triangles, J. Algebr. Comb. 52 (2020), 339-368.

23. M. Bonini, M. Montanucci and G. Zini , On plane curves given by separated polynomials and applications, Adv. Geom., 20 (2020), 61-70.

22. G. Korchmáros and M. Montanucci, Large odd prime power order automorphism groups of algebraic curves in any characteristic, J. Algebra 574 (2020), 312-344.

21. M. Montanucci and G. Zini, The complete list of genera of quotients of the F_{q^2}-maximal Hermitian curve for q = 1 mod 4, J. Algebra 550 (2020), 23-53.

20. M. Montanucci and P. Speziali, Large automorphism groups of ordinary curves of even genus in odd characteristic, Comm. Algebra 48 (2020), 3690-3706.

19. G. Marino, M. Montanucci and F. Zullo, MRD-codes arising from the trinomial $x^q+x^{q^3}+cx^{q^5} \in \mathbb{F}_{q^6}[x]$, Linear Algebra and its Appl. 591 (2020), 99-114.

18. G. Korchmáros and M. Montanucci, Ordinary algebraic curves with many automorphisms in positive characteristic, Algebra and Number Theory 13 (2019), 1-18.

17. M. Montanucci and P. Speziali, Large automorphism groups of ordinary curves in characteristic 2, J. Algebra 526 (2019), 30-50.

16. F. Dalla Volta, M. Montanucci and G. Zini, On the classification problem for the genera of quotients of the Hermitian curve, Comm. Algebra 47 (2019), 4889-4909.

15. D. Bartoli, M. Giulietti and M. Montanucci, Linear codes from Denniston maximal arcs, Des. Codes Cryptogr. 87 (2019), 795-806.

14. M. Montanucci, G. Zini and M. Timpanella, AG codes and AG quantum codes from cyclic extensions of the Suzuki and the Ree curves, J. Geom. 109 (2018), no. 1, 18 pp.

13. P. Beelen and M. Montanucci, Weierstrass semigroups on the Giulietti-Korchmáros curve, Finite Fields Appl. 52}(2018), 10-29.

12. P. Beelen and M. Montanucci, A new family of maximal curves, Journal of the London Math. Soc. 98 (2018), 573-592.

11. D. Bartoli, A. Masuda, M. Montanucci and L. Quoos, Pure gaps on curves with many rational points, Finite Fields Appl. 53 (2018), 287-308.

10. D. Bartoli, M. Montanucci and G. Zini, AG codes and AG quantum codes from the GGS curve, Des. Codes Cryptogr., 86 (2018), 2315-2344.

9. M. Giulietti, M. Montanucci, L. Quoos and G. Zini, The automorphism group of some Galois covers of the Suzuki and Ree curves, J. Number Theory 189 (2018), 220-254.

8. M. Montanucci and G. Zini, On the spectrum of genera of Galois subcovers of the Hermitian curve, Comm. Algebra 46 (2018), 4739-4776.

7. M. Montanucci and P. Speziali, The a-numbers of Fermat and Hurwitz curves, J. Pure Appl. Algebra 2 (2018), 477-488.

6. G. Korchmáros, M. Montanucci and P. Speziali, Transcendence Degree One Function Fields Over a Finite Field with Many Automorphisms, J. Pure Appl. Algebra 222 (2018), 1810-1826.

5. D. Bartoli, M. Montanucci and G. Zini, Multi-Point AG Codes on the GK Maximal Curve, Des. Codes Cryptogr. 3 (2017), 1-17.

4. M. Montanucci and G. Zini, Generalized Artin-Mumford curves over finite fields, J. Algebra 485 (2017), 310-331.

3. M. Montanucci and G. Zini, Some Ree and Suzuki curves are not Galois covered by the Hermitian curve, Finite Fields Appl. 48 (2017), 175-195.

2. G. Korchmáros and M. Montanucci, The Geometry of the Artin-Schreier-Mumford Curves over an Algebraically Closed Field, Acta Sci. Math., (Szeged) 83:3-4 (2017), 673-681.

1. M. Giulietti, M. Montanucci and G. Zini, On maximal curves that are not quotients of the Hermitian curve, Finite Fields Appl. 41 (2016), 72-88.

CONFERENCE PUBLICATIONS

1. P. Beelen, M. Montanucci and L. Vicino, On the constant $D(q)$ defined by Homma, Arithmetic, geometry, cryptography, and coding theory 2021, 33-40. Contemp. Math.,

779 American Mathematical Society, Providence, RI, 2022.

2. M. Giulietti, G. Korchmaros and M. Montanucci,Maximal curves over nite elds, past, present and future. Curves over finite fields: past, present and future, 37-66. Panor.

Syntheses, 60 Societe Mathematique de France, Paris, 2023.

3. P. Beelen, R. Con, A. Gruica, M. Montanucci and E. Yaakobi, Reed-Solomon Codes Against Insertions and Deletions: Full-Length and Rate-1/2 Codes, 2025 IEEE International Symposium on Information Theory (ISIT), Ann Arbor, MI, USA (2025), pp. 1-6.

PREPRINTS

1. D. Bartoli, M. Montanucci and G. Zini, Bent functions from triples of permutation polynomials.

2. P. Beelen and M. Montanucci, A Bound for the number of points of space curves over finite fields.

3. P. Beelen, L. Landi and M. Montanucci, Classification of all Galois subcovers of the Skabelund maximal curves.

4. M. Montanucci and G. Tiziotti, Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve.

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