Publications

You can see my publications on ResearchGate. You can also see them on Scopus or Google Scholar.

  1. E. E. Alberdi, S. Alkan, N. Anbar, A. Avrantini, T. Kalaycı, B. Toesca:
    On decomposition of bent functions, in preparation.
  2. N. Anbar, T. Kalaycı, W. Meidl, A. Polujan:
    On the almost balancedness of generalized bent functions, in preparation.
  3. N. Anbar, T. Kalaycı, S. Kudin, W. Meidl, A. Polujan, E. Pasalic, F. Zhang:
    Concatenating bent functions in PS_{ap} class and related M-subspaces, in preparation.
  4. N. Anbar, T. Kalaycı, W. Meidl:
    A survey on bent partitions, submitted.
  5. N. Anbar, T. Kalaycı:
    Further results on association schemes from non-weakly regular bent functions, submitted.
  6. N. Anbar, F.-W. Fu, T. Kalaycı, W. Meidl, J. Wang, Y. Wei:
    Analysis of some classes of bent partitions and vectorial bent functions, Journal of Designs, Codes and Cryptography, to appear.
  7. N. Anbar, T. Kalaycı, W. Meidl, F. Özbudak:
    Vectorial dual-bent functions and association schemes, Journal of Designs, Codes and Cryptography, to appear.
  8. N. Anbar, T. Kalaycı, W. Meidl, F. Özbudak:
    Bent partitions and Maiorana-McFarland association schemes, Cryptography and Communications,  17 (2025), 1641–1657.
    DOI: 10.1007/s12095-025-00801-x
  9. N. Anbar, T. Kalaycı, A. Topuzoğlu:
    Analysis of functions of low differential uniformity in characteristic 2: A new approach (I), IEEE Transactions on Information Theory, 71 (2025), no. 10, 8002-8016.
    DOI: 10.1109/TIT.2025.3597162
  10. N. Anbar, T. Kalaycı, N. Yurdakul:
    On the classification of non-exceptional APN functions, Applicable Algebra Engineering Communication and Computing, 36 (2025), 847–861.
    DOI: 10.1007/s00200-023-00642-2
  11. N. Anbar, S. Kudin, W. Meidl , E. Pasalic, A. Polujan:
    Vectorial negabent concepts: Similarities, differences, and generalizations, Journal of Designs, Codes and Cryptography, 93 (2025), 899–921.
    DOI: 10.1007/s10623-024-01454-2
  12. N. Anbar, T. Kalaycı, W. Meidl, F. Özbudak:
    (2p + 1)-class association schemes from the generalized Maiorana-McFarland class    , Finite Fields and their Applications, 103 (2025), 102568, 32 pp.
    DOI: 10.1016/j.ffa.2024.102568
  13. S. Alkan, N. Anbar, T. Kalaycı, W. Meidl:
    Bent partition, vectorial dual-bent function and LP-packing constructions, IEEE Transactions on Information Theory, 71 (2025), no. 1, 752-767.
    DOI: 10.1109/TIT.2024.3505600
  14. N. Anbar: 
    On a special type of permutation rational     functions, Applicable Algebra Engineering Communication and Computing, 35 (2024), 821–832.
    DOI: 10.1007/s00200-022-00592-1
  15. S. Alkan, N. Anbar, T. Kalaycı, W. Meidl:
    Bent partitions and LP-packings, IEEE Transactions on Information Theory, 70 (2024), no. 7, 5365-5375.
    DOI: 10.1109/TIT.2024.3359260
  16. N. Anbar, T. Kalaycı, W. Meidl:
    Amorphic association schemes from bent partitions, Discrete Mathematics, 347 (2024), no. 1, 113658, 13pp.
    DOI: 10.1016/j.disc.2023.113658
  17. N. Anbar, T. Kalaycı, W. Meidl:
    On generalized spread bent partitions, Cryptography and Communications, 15 (2023), 1217-1234.
    DOI: 10.1007/s12095-023-00670-2
  18. N. Anbar, T. Kalaycı, W. Meidl, C. Riera, P. Stanica:
    P℘N functions, complete mappings and quasigroup difference sets, Journal of Combinatorial Designs, 31 (2023), 667-690.
    DOI: 10.1002/jcd.21916
  19. N. Anbar, T. Kalaycı, W. Meidl:
    Generalized semifield spreads, Journal of Designs, Codes and Cryptography, 91 (2023), 545-562.
    DOI: 10.1007/s10623-022-01115-2
  20. N. Anbar, T. Kalaycı, W. Meidl:
    Bent partitions and partial difference sets, IEEE Transactions on Information Theory, 68 (2022), no. 10, 6894-6903.
    DOI: 10.1109/TIT.2022.3177003
  21. N. Anbar, T. Kalaycı, W. Meidl, L. Merai:
    On a class of functions with the maximal number of bent components, IEEE Transactions on Information Theory, 68 (2022), no. 9, 6174-6186.
    DOI: 10.1109/TIT.2022.3174672
  22. N. Anbar, W. Meidl:
    Bent partitions, Journal of Designs, Codes and Cryptography, 90 (2022), 1081-1101.
    DOI: 10.1007/s10623-022-01029-z
  23. N. Anbar, B. Güneş:
    On nilpotent automorphism groups of function fields, Advances in Geometry, 22 (2022), no. 1, 69-78.
    DOI: 10.1515/advgeom-2021-0006
  24. N. Anbar, T. Kalaycı, A. Topuzoğlu:
    On partially APN functions, presented at the 12th International Workshop on Coding and Cryptography 2022, WCC2022.
    https://www.wcc2022.uni-rostock.de/storages/uni-rostock/Tagungen/WCC2022/Papers/WCC_2022_paper_27.pdf
  25. N. Anbar, T. Kalaycı, N. Yurdakul:
    Note on exceptional APN functions of Gold and Kasami-Welch type, presented at the 12th International Workshop on Coding and Cryptography 2022, WCC2022.
    https://www.wcc2022.uni-rostock.de/storages/uni-rostock/Tagungen/WCC2022/Papers/WCC_2022_paper_64.pdf
  26. N. Anbar, H. Stichtenoth, S. Tutdere:
    Asymptotically good towers of function fields with small p-rank, Finite Fields and their Applications, 76 (2021), 101909, 13pp.
    DOI: 10.1016/j.ffa.2021.1001909
  27. N. Anbar, T. Kalaycı, W. Meidl:
    Analysis of (n,n)-functions obtained from the Maiorana-McFarland class, IEEE Transactions on Information Theory, 67 (2021), no. 7, 4891-4901.
    DOI: 10.1109/TIT.2021.3079223
  28. N. Anbar, C. Kaşıkçı:
    Permutations polynomials of the form G(x)^k −L(x) and curves over finite fields, Cryptography and Communications, 13 (2021), no. 2, 283-294.
    DOI: 10.1007/s12095-020-00465-9
  29. N. Anbar, C. Kaşıkçı, W. Meidl, A. Topuzoğlu:
    Shifted plateaued functions and their differential properties, Cryptography and Communications, 12 (2020), 1091–1105.
    DOI: 10.1007/s12095-020-00426-2
  30. N. Anbar, S. Tutdere:
    Belyi’s theorem in positive characteristic, International Journal of Number Theory, 16 (2020), no. 6, 1355-1368.
    DOI: 10.1142/s1793042120500712
  31. N. Anbar, W. Meidl, A. Pott:
    Equivalence for negabent functions and their relative difference sets, Discrete Applied Mathematics, 270 (2019), 1-12.
    DOI: 10.1016/j.dam.2019.07.018
  32. N. Anbar, T. Kalaycı, W. Meidl:
    Determining the Walsh spectra of Taniguchi’s and related APN-functions, Finite Fields and their Applications, 60 (2019), 101577, 20pp.
    DOI: 10.1016/j.ffa.2019.101577
  33. N. Anbar, C. Kaşıkçı, A. Topuzoğlu:
    On components of vectorial permutations of F_q^n, Finite Fields and their Applications, 58 (2019), 124-132.
    DOI: 10.1016/j.ffa.2019.03.006
  34. N. Anbar:
    Curves over finite fields and permutations of the form x^k- \gamma Tr(x), Turkish Journal of Mathematics, 43 (2019), 533-538.
    DOI: 10.3906/MAT-1811-27
  35. N. Anbar, A. Ozdak, V. Patel, L. Quoos, A. Somoza, A. Topuzoğlu:
    On the Carlitz rank of permutation polynomials over finite fields: Recent developments, In: Bouw I., Özman E., Johnson-Leung J., Newton R. (eds) Women in Number Europe II. Association for Women in Mathematics Series, 11 (2018) Springer, Cham, 39-55.
    DOI: 10.1007/978-3-319-74998-3_4
  36. N. Anbar, W. Meidl:
    Modified planar functions and their components, Cryptography and Communications, 10 (2018), no. 2, 235-249.
    DOI: 10.1007/s12095-017-0218-9
  37. N. Anbar, A. Ozdak, V. Patel, L. Quoos, A. Somoza, A. Topuzoğlu:
    On the difference between permutation polynomials, Finite Fields and their Applications, 49 (2018), 132-142.
    DOI: 10.1016/j.ffa.2017.09.009
  38. N. Anbar, P Beelen:
    A note on a tower by Bassa, Garcia and Stichtenoth, Functiones et Approximatio Commentarii Mathematici, 57 (2017), no. 1, 47-60.
    DOI: 10.7169/facm/1615
  39. N. Anbar, A. Bassa, P. Beelen:
    A complete characterization of Galois subfields of the generalized Giulietti-Korchmaros function field, Finite Fields and their Applications, 48 (2017), 318-330.
    DOI: 10.1016/j.ffa.2017.08.006
  40. N. Anbar, W. Meidl:
    Bent and Bent_4 spectra of quadratic functions over F_{2^n}, Finite Fields and their Applications, 46 (2017), 163-178.
    DOI: 10.1016/j.ffa.2017.03.008
  41. N. Anbar, P. Beelen, N. Nguyen:
    The exact limit of some cubic towers, in Arithmetic, geometry, cryptography and coding theory (AGCT 2015), Contemp. Math., 686 (2017), 1-15.
    DOI: 10.1090/conm/686/13774
  42. N. Anbar, P. Beelen, N. Nguyen:
    A new tower meeting Zink’s bound with good p-rank, Acta Arithmetica, 177 (2017), no. 4, 347-374.
    DOI: 10.4064/aa8388-6-2016
  43. N. Anbar, A. Bassa, P. Beelen:
    A modular interpretation of various cubic towers, Journal of Number Theory, 171 (2017), 341-357.
    DOI: 10.1016/j.jnt.2016.07.025
  44. N. Anbar, W. Meidl, A. Topuzoglu:
    Idempotent and p-potent quadratic functions: Distribution of nonlinearity and co-dimension, Journal of Designs, Codes and Cryptography 82 (2017), no.1, 265-291.
    DOI: 10.1007/s10623-016-0213-8
  45. N. Anbar, W. Meidl, A. Topuzoğlu:
    On the nonlinearity of idempotent quadratic functions and the weight distribution of subcodes of Reed-Muller codes, Proceedings of the 9th International Workshop on Coding and Cryptography 2015.
    https://hal.inria.fr/hal-01276432
  46. N. Anbar, W. Meidl:
    More on Quadratic functions and maximal Artin-Schreier curves, Applicable Algebra Engineering Communication and Computing, 26 (2015), no.5, 409-426.
    DOI: 10.1007/s00200-015-0259-2
  47. N. Anbar, D. Bartoli, M. Giulietti, I. Platoni:
    Small complete caps from singular cubics, II,  Journal of Algebraic Combinatorics, 41 (2015), no.1, 185-216.
    DOI: 10.1007/s10801-014-0532-7
  48. N. Anbar, W. Meidl:
    Quadratic functions and maximal Artin-Schreier curves, Finite Fields and their Applications, 30 (2014), 49-71.
    DOI: 10.1016/j.ffa.2014.05.008
  49. N. Anbar, D. Bartoli, M. Giulietti, I. Platoni:
    Small complete caps from singular cubics, Journal of Combinatorial Designs, 22 (2014), no.10, 409-424.
    DOI: 10.1002/jcd.21366
  50. N. Anbar W. Meidl:
    Quadratic functions and Artin-Schreier curves in odd characteristic,  Max-Planck-Institut für Mathematik, Preprint Series 2014 (36)
  51. N. Anbar, H. Stichtenoth:
    On the number of rational points, Electronic Notes in Discrete Mathematics, 40 (2013), 21-26.
    DOI: 10.1016/j.endm.2013.05.005
  52. N. Anbar, D. Bartoli, S. Fanali, M. Giulietti:
    On the size of the automorphism group of a plane algebraic curve, Journal of Pure and Applied Algebra, 217 (2013), no.7, 1224 -1236.
    DOI: 10.1016/j.jpaa.2012.10.011
  53. N. Anbar, H. Stichtenoth:
    Curves of every genus with a prescribed number of rational points, Bulletin of the Brazilian Mathematical Society, 44 (2013), no.2, 173-193.
    DOI: 10.1007/s00574-013-0008-8
  54. N. Anbar, M. Giulietti:
    Bicovering arcs and small complete caps from elliptic curves, Journal of Algebraic Combinatorics, 38 (2013), no. 2, 371-392.
    DOI: 10.1007/s10801-012-0407-8
  55. N. Anbar, H. Stichtenoth, S. Tutdere:
    On ramification in the compositum of function fields, Bulletin of the Brazilian Mathematical Society, 40 (2009), no.4, 539 -552.
    DOI: 10.1007/s00574-009-0026-8

Working Papers

  1. N. Anbar, D. Bartoli, I. Platoni, M. Giulietti:
    Complete arcs and complete caps from cubics with an isolated double point, preprint.
    ArXiv: 1305.3420.
  2. N. Anbar, D. Bartoli, I. Platoni, M. Giulietti:
    Small complete caps from nodal cubics, preprint.
    ArXiv: 1305.3019.

Thesis

  1. Ph.D., 2012: On algebraic curves in prime characteristic

  2. M.Sc., 2009: On ramification in extensions of rational function fields

 

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