Publications

You can see my publications on Researchgate. Also, you may see them on Scopus or Google Scholar.

  1. S. Alkan, N. Anbar, T. Kalaycı, W. Meidl:
    Bent partition, vectorial dual-bent function and LP-packing constructions, submitted.
  2. N. Anbar, T. Kalaycı, W. Meidl, F. Özbudak:
    (2p + 1)-class association schemes from the generalized Maiorana Mc-Farland class    , submitted.
  3. N. Anbar, S. Kudin, W. Meidl , E. Pasalic, A. Polujan:
    Vectorial negabent concepts: Similarities, differences, and generalizations, submitted.
  4. N. Anbar, T. Kalaycı, W. Meidl, F. Özbudak:
    Vectorial dual-bent functions and association schemes, submitted.
  5. N. Anbar, T. Kalaycı, A. Topuzoğlu:
    Modified functions with low differential uniformity: Refined measures of planarity over F_{2^n} and infinitely many extensions, submitted.
  6. N. Anbar, T. Kalaycı, N. Yurdakul:
    On the classification of non-exceptional APN functions, Applicable Algebra Engineering Communication and Computing, to appear.
    DOI: 10.1007/s00200-023-00642-2
  7. S. Alkan, N. Anbar, T. Kalaycı, W. Meidl:
    Bent partitions and LP-packings, IEEE Transactions on Information Theory, to appear.
    DOI: 10.1109/TIT.2024.3359260
  8. N. Anbar: 
    On a special type of permutation rational     functions, Applicable Algebra Engineering Communication and Computing, to appear.
    DOI: 10.1007/s00200-022-00592-1
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. N. Anbar, W. Meidl:
    Bent partitions, Journal of Designs, Codes and Cryptography, 90 (2022), 1081-1101.
    DOI: 10.1007/s10623-022-01029-z
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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
  26. 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
  27. 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
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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
  40. 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
  41. 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
  42. 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
  43. N. Anbar W. Meidl:
    Quadratic functions and Artin-Schreier curves in odd characteristic,  Max-Planck-Institut für Mathematik, Preprint Series 2014 (36)
  44. 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
  45. 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
  46. 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
  47. 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
  48. 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

 

➤