Mathematics, Algebra and Number Theory, Applied Mathematics
31
Scopus Publications
429
Scholar Citations
12
Scholar h-index
14
Scholar i10-index
Scopus Publications
Cyclotomic function fields over finite fields with irreducible quadratic modulus Nazar Arakelian, Luciane Quoos Advances in Geometry, 2026 Let 𝔽 q be the finite field of order q and F = 𝔽 q ( x ) the rational function field. In this paper, we give a characterization of the cyclotomic function fields F ( Λ M ) with modulus M , where M ∈ 𝔽 q [ T ] is a monic and irreducible polynomial of degree two. More precisely, we show that F ( Λ M ) is the only function field, up to 𝔽 q -isomorphism, with q + 1 𝔽 q -rational places, genus ( q + 1)( q − 2)/2 and a subgroup of automorphisms over 𝔽 q isomorphic to F q 2 ∗ . $\\mathbb{F}_{q^2}^*.$ We also provide the full automorphism group of F ( Λ M ) in odd characteristic, extending results of [14] where the automorphism group of F ( Λ M ) over 𝔽 q was computed.
A family of non-isomorphic maximal function fields Peter Beelen, Maria Montanucci, Jonathan Niemann, Luciane Quoos Mathematische Zeitschrift, 2025 The problem of understanding whether two given function fields are isomorphic is well-known to be difficult, particularly when the aim is to prove that an isomorphism does not exist. In this paper we investigate a family of maximal function fields that arise as Galois subfields of the Hermitian function field. We compute the automorphism group, the Weierstrass semigroup at some special rational places and the isomorphism classes of such function fields. In this way, we show that often these function fields provide in fact examples of maximal function fields with the same genus, the same automorphism group, but that are not isomorphic.
Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field A. S. Castellanos, L. Quoos, G. Tizziotti Journal of Algebra and Its Applications, 2024 For [Formula: see text] an odd integer, we provide a sequence from the function field [Formula: see text] of the maximal curve over [Formula: see text] defined by the affine equation [Formula: see text]. This sequence has high nonlinear complexity, and this fact comes from the existence of a rational function on [Formula: see text] with pole divisor of small degree, and support in certain [Formula: see text] rational places.
Characterization of non-special divisors of small degree on Kummer extensions and LCP codes E Mendoza, H Navarro, L Quoos arXiv preprint arXiv:2604.27146 , 2026 2026 Citations: 1
Cyclotomic function fields over finite fields with irreducible quadratic modulus N Arakelian, L Quoos Advances in Geometry 26 (2), 149-161 , 2026 2026
A closed formula for the Geil-Matsumoto bound on numerical semigroups A Marques, E Mendoza, L Quoos, G Tizziotti arXiv preprint arXiv:2508.17022 , 2025 2025
Sequences of LCD AG codes and LCP of AG Codes attaining the Tsfasman-Vladut-Zink bound A Marques, L Quoos arXiv preprint arXiv:2505.23937 , 2025 2025
Good iso-dual AG-codes from towers of function fields M Chara, R Podestá, L Quoos, R Toledano arXiv preprint arXiv:2503.08899 , 2025 2025 Citations: 2
A family of non-isomorphic maximal function fields P Beelen, M Montanucci, J Niemann, L Quoos Mathematische Zeitschrift 309 (2), 19 , 2025 2025 Citations: 5
Linear complementary dual codes and linear complementary pairs of AG codes in function fields AS Castellanos, AV Marques, L Quoos IEEE Transactions on Information Theory 71 (3), 1676-1688 , 2024 2024 Citations: 7
Lifting iso-dual algebraic geometry codes M Chara, R Podestá, L Quoos, R Toledano Designs, Codes and Cryptography 92 (10), 2743-2767 , 2024 2024 Citations: 5
Self-orthogonal flags of codes and translation of flags of algebraic geometry codes M Bras-Amorós, AS Castellanos, L Quoos arXiv preprint arXiv:2406.08952 , 2024 2024
Some classes of permutation binomials and trinomials of index over R Gupta, L Quoos, Q Wang Cryptography and Communications 16 (2), 387-402 , 2024 2024
Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field AS Castellanos, L Quoos, G Tizziotti Journal of Algebra and Its Applications 23 (02), 2450037 , 2024 2024 Citations: 7
Isometry-dual flags of many-point AG codes M Bras-Amorós, AS Castellanos, L Quoos SIAM Journal on Applied Algebra and Geometry 7 (4), 786-808 , 2023 2023 Citations: 2
Classification of some permutation quadrinomials from self reciprocal polynomials over F2n FEB Martínez, R Gupta, L Quoos Finite Fields and Their Applications 91, 102276 , 2023 2023 Citations: 7
Reciprocal polynomials and curves with many points over a finite field R Gupta, EAR Mendoza, L Quoos Research in Number Theory 9 (3), 60 , 2023 2023 Citations: 8
Weierstrass Semigroups, Pure Gaps and Codes on Function Fields AS Castellanos, EAR Mendoza, L Quoos arxiv.org/pdf/2304.02128 , 2023 2023 Citations: 11
Explicit equations for maximal curves as subcovers of the BM curve EAR Mendoza, L Quoos Finite Fields and Their Applications 77, 101945 , 2022 2022 Citations: 9
The isometry-dual property in flags of two-point algebraic geometry codes M Bras-Amorós, AS Castellanos, L Quoos IEEE Transactions on Information Theory 68 (2), 828-838 , 2021 2021 Citations: 4
Rational functions with small value set D Bartoli, H Borges, L Quoos Journal of Algebra 565, 675-690 , 2021 2021 Citations: 5
Locally Recoverable Codes From Automorphism Group of Function Fields of Genus g ≥ 1 D Bartoli, M Montanucci, L Quoos IEEE Transactions on Information Theory 66 (11), 6799-6808 , 2020 2020 Citations: 21
Weierstrass points on Kummer extensions M Abdón, H Borges, L Quoos Advances in Geometry 19 (3), 323-333 , 2019 2019 Citations: 23
MOST CITED SCHOLAR PUBLICATIONS
One-and two-point codes over Kummer extensions AS Castellanos, AM Masuda, L Quoos IEEE Transactions on Information Theory 62 (9), 4867-4872 , 2016 2016 Citations: 38
Complete permutation polynomials from exceptional polynomials D Bartoli, M Giulietti, L Quoos, G Zini Journal of Number Theory 176, 46-66 , 2017 2017 Citations: 36
Further examples of maximal curves M Abdón, J Bezerra, L Quoos Journal of Pure and Applied Algebra 213 (6), 1192-1196 , 2009 2009 Citations: 33
A construction of curves over finite fields A Garcia, L Quoos Acta Arithmetica 98, 181-195 , 2001 2001 Citations: 28
On the genera of subfields of the Hermitian function field M Abdon, L Quoos Finite Fields and Their Applications 10 (3), 271-284 , 2004 2004 Citations: 27
Weierstrass points on Kummer extensions M Abdón, H Borges, L Quoos Advances in Geometry 19 (3), 323-333 , 2019 2019 Citations: 23
Permutation polynomials of the type over D Bartoli, L Quoos Designs, Codes and Cryptography 86 (8), 1589-1599 , 2018 2018 Citations: 22
Locally Recoverable Codes From Automorphism Group of Function Fields of Genus g ≥ 1 D Bartoli, M Montanucci, L Quoos IEEE Transactions on Information Theory 66 (11), 6799-6808 , 2020 2020 Citations: 21
On some Galois covers of the Suzuki and Ree curves M Giulietti, M Montanucci, L Quoos, G Zini Journal of Number Theory 189, 220-254 , 2018 2018 Citations: 20
Maximal curves from subcovers of the GK-curve M Giulietti, L Quoos, G Zini Journal of Pure and Applied Algebra 220 (10), 3372-3383 , 2016 2016 Citations: 20
On the difference between permutation polynomials N Anbar, A Odzak, V Patel, L Quoos, A Somoza, A Topuzoğlu Finite Fields and Their Applications 49, 132-142 , 2018 2018 Citations: 17
Algebraic geometric codes on many points from Kummer extensions D Bartoli, L Quoos, G Zini Finite Fields and Their Applications 52, 319-335 , 2018 2018 Citations: 16
Weierstrass Semigroups, Pure Gaps and Codes on Function Fields AS Castellanos, EAR Mendoza, L Quoos arxiv.org/pdf/2304.02128 , 2023 2023 Citations: 11
Character theory of monoids over an arbitrary field AM Masuda, L Quoos, B Steinberg Journal of Algebra 431, 107-126 , 2015 2015 Citations: 10
Explicit equations for maximal curves as subcovers of the BM curve EAR Mendoza, L Quoos Finite Fields and Their Applications 77, 101945 , 2022 2022 Citations: 9
Pure gaps on curves with many rational places D Bartoli, AM Masuda, M Montanucci, L Quoos Finite Fields and Their Applications 53, 287-308 , 2018 2018 Citations: 9
On the Carlitz rank of permutation polynomials over finite fields: recent developments N Anbar, A Odžak, V Patel, L Quoos, A Somoza, A Topuzoğlu Women in Numbers Europe II: Contributions to Number Theory and Arithmetic … , 2018 2018 Citations: 9
Reciprocal polynomials and curves with many points over a finite field R Gupta, EAR Mendoza, L Quoos Research in Number Theory 9 (3), 60 , 2023 2023 Citations: 8
Linear complementary dual codes and linear complementary pairs of AG codes in function fields AS Castellanos, AV Marques, L Quoos IEEE Transactions on Information Theory 71 (3), 1676-1688 , 2024 2024 Citations: 7
Construction of sequences with high nonlinear complexity from a generalization of the Hermitian function field AS Castellanos, L Quoos, G Tizziotti Journal of Algebra and Its Applications 23 (02), 2450037 , 2024 2024 Citations: 7
