On the irreducibility of the hyperplane sections of Fermat varieties in P3\mathbb {P}^{3}P3 in characteristic 2. II (original) (raw)

References

1. Aubry, Y., McGuire, G., Rodier, F.: A few more functions that are not APN infinitely often Finite fields: Theory and applications, Contemporary Mathematics 518, pp. 23–31. American Mathematical Society, Providence, RI (2010)
   Chapter Google Scholar
2. Berger, T., Canteaut, A., Charpin, P., Laigle-Chapuy, Y.: On almost perfect nonlinear functions over \(F^n_{2}\). IEEE Trans. Inf. Theory 52(9), 4160–4170 (2006)
   Article MATH Google Scholar
3. Bluher, A. W.: On existence of Budaghyan-Carlet APN hexanomials. Finite Fields Appl. 24, 118–123 (2013)
   Article MathSciNet MATH Google Scholar
4. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language, Computational algebra and number theory (London, 1993). J. Symb. Comput. 24(3–4), 235–265 (1997)
   Article MATH Google Scholar
5. Bracken, C., Byrne, E., Markin, N., McGuire, G.: New families of quadratic almost perfect nonlinear trinomials and multinomials. Finite Fields Appl. 14 (3), 703–714 (2008)
   Article MathSciNet MATH Google Scholar
6. Bracken, C., Tan, C. H., Tan, Y.: On a class of quadratic polynomials with no zeros and its application to APN functions. Finite Fields Appl. 25, 26–36 (2014)
   Article MathSciNet MATH Google Scholar
7. Budaghyan, L., Carlet, C., Felke, P., Leander, G.: An infinite class of quadratic APN functions which are not equivalent to power mappings. In: Proceedings of the IEEE International Symposium on Information Theory, pp. 2637–2641 (2006)
8. Byrne, E., McGuire, G.: On the non-existence of quadratic APN and crooked functions on finite fields. In: Proceedings of the Workshop on Coding and Cryptography, WCC, pp. 316–324 (2005)
9. Caullery, F.: A new large class of functions not APN infinitely often. Des. Codes Cryptogr. 73(2), 601–614 (2014)
   Article MathSciNet MATH Google Scholar
10. Caullery, F.: Polynomials over finite fields for cryptography. Ph.D. thesis, Université d’Aix-Marseille. http://www.theses.fr/2014AIXM4013 (2014)
11. Carlet, C., Charpin, P., Zinoviev, V.: Codes, bent functions and permutations suitable for DES-like cryptosystems. Des. Codes Cryptogr. 15(2), 125–156 (1998)
    Article MathSciNet MATH Google Scholar
12. Dillon, J.F.: APN Polynomials: An update. Invited talk at Fq9 the 9th International Conference on Finite Fields and their Applications (2009)
13. Delgado, M., Janwa, H.: On the conjecture on APN functions. arXiv:1207.5528 [cs.IT]
14. Edel, Y., Kyureghyan, G., Pott, A.: A new APN function which is not equivalent to a power mapping. IEEE Trans. Inform. Theory 52(2), 744–747 (2006)
    Article MathSciNet MATH Google Scholar
15. Férard, E.: On the irreducibility of the hyperplane sections of Fermat varieties in \(\mathbb {P}^{3}\) in characteristic 2. Adv. Math. Commun. 8(4), 497–509 (2014)
    Article MathSciNet MATH Google Scholar
16. Férard, E.: A infinite class of Kasami functions that are not APN infinitely often. Submitted to AGCT 15
17. Férard, E., Oyono, R., Rodier, F.: Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents Arithmetic, geometry, cryptography and coding theory, Contemporary Mathematics, 574, pp. 27–36. American Mathematical Society, Providence, RI (2012)
    Chapter Google Scholar
18. Férard, E., Rodier, F.: Non linéarité des fonctions booléennes données par des polynômes de degré binaire 3 définies sur \(\mathbb {F}_2^{m}\) avec m pair [Nonlinearity of Boolean functions given by polynomials of binary degree 3 defined on \(\mathbb {F}_2^{m}\) with m even] Arithmetic, geometry, cryptography and coding theory 2009, Contemporary Mathematics, 521, pp. 41–53. American Mathematical Society, Providence, RI (2010)
    Chapter Google Scholar
19. Férard, E., Rodier, F.: Non linéarité des fonctions booléennes données par des traces de polynômes de degré binaire 3 [Nonlinearity of Boolean functions given by traces of polynomials of binary degree 3]. Algebraic geometry and its applications, Series Number Theory Applications, 5, pp. 388–409. World Scientific Publications, Hackensack, NJ (2008)
20. Hernando, F., McGuire, G.: Proof of a conjecture on the sequence of exceptional numbers, classifying cyclic codes and APN functions. J. Algebra 343, 78–92 (2011)
    Article MathSciNet MATH Google Scholar
21. Fulton, W.: Algebraic curves. Benjamin New York (1969)
22. Janwa, H., Wilson, R.M.: Hyperplane sections of Fermat varieties in P 3 in char. 2 and some applications to cyclic codes. In: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Proceedings AAECC-10 (G. Cohen, T. Mora and O. Moreno Eds.), Lecture Notes in Computer Science, vol. 673, pp. 180194. Springer-Verlag, NewYork/Berlin (1993)
23. Janwa, H., McGuire, G., Wilson, R.M.: Double-error-correcting cyclic codes and absolutely irreducible polynomials over GF(2). J. Algebra 178, 665–676 (1995)
    Article MathSciNet MATH Google Scholar
24. Jedlicka, D.: APN monomials over G F(2_n_) for infinitely many n. Finite Fields Appl. 13(4), 1006–1028 (2007)
    Article MathSciNet MATH Google Scholar
25. Lucas, E.: Théorie des fonctions numériques simplement périodiques. Amer. J. Math. 1, 197–240, 289–321 (1878)
    Article MathSciNet Google Scholar
26. Nyberg, K.: Differentially uniform mappings for cryptography Advances in cryptology—Eurocrypt ’93 (Lofthus, 1993), Lecture Notes in Computer Science, vol. 765, pp. 55–64. Springer, Berlin (1994)
    Google Scholar
27. Rodier, F.: Bornes sur le degré des polynômes presque parfaitement non-linéaires Arithmetic, Geometry, Cryptography and Coding Theory, Contemporary Mathematics 487, pp. 169–181. American Mathematical Society, Providence, RI (2009)
    Chapter Google Scholar
28. Rodier, F.: Functions of degree 4_e_ that are not APN infinitely often. Cryptogr. Commun. 3, 227–240 (2011)
    Article MathSciNet MATH Google Scholar
29. Stein, W.A., et al.: Sage Mathematics Software (Version 4.8) The Sage Development Team. http://www.sagemath.org (2012)

Download references