[1]
|
A. Canteaut, P. Charpin and G. M. Kyureghyan, A new class of monomial bent functions, Finite Fields and Their Applications, 14 (2008), 221-241.
doi: 10.1016/j.ffa.2007.02.004.
|
[2]
|
C. Carlet, Boolean Functions for Cryptography and Coding Theory, Cambridge University Press, Cambridge, 2020.
doi: 10.1017/9781108606806.
|
[3]
|
C. Carlet, Boolean functions for cryptography and error-correcting codes, in Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge University Press, Cambridge, (2010), 257-397.
doi: 10.1017/CBO9780511780448.
|
[4]
|
C. Carlet, Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications, IEEE Transactions on Information Theory, 54 (2008), 1262-1272.
doi: 10.1109/TIT.2007.915704.
|
[5]
|
G. Cohen, I. Honkala and S. Litsyn, Covering Codes, North-Holland, Amsterdam, 1997.
|
[6]
|
H. Dobbertin, G. Leander, A. Canteaut, C. Carlet, P. Felke and P. Gaborit, Construction of bent functions via Niho power functions, Journal of Combinatorial Theory, Series A, 113 (2006), 779-798.
doi: 10.1016/j.jcta.2005.07.009.
|
[7]
|
I. Dumer, G. Kabatiansky and C. Tavernier, List decoding of Reed-Muller codes up to the Johnson bound with almost linear complexity, 2006 IEEE International Symposium on Information Theory, (2006), 138-142.
doi: 10.1109/ISIT.2006.261690.
|
[8]
|
R. Fourquet and C. Tavernier, An improved list decoding algorithm for the second order Reed-Muller codes and its applications, Designs Codes and Cyptography, 49 (2008), 323-340.
doi: 10.1007/s10623-008-9184-8.
|
[9]
|
S. Gangopadhyay, S. Sarkar and R. Telang, On the lower bounds of the second order nonlinearities of some Boolean functions, Information Sciences, 180 (2010), 266-273.
doi: 10.1016/j.ins.2009.09.006.
|
[10]
|
Q. Gao and D. Tang, A lower bound on the second-order nonlinearity of the generalized Maiorana-McFarland Boolean functions, IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, E101.A (2018), 2397-2401.
doi: 10.1587/transfun.E101.A.2397.
|
[11]
|
R. Gode and S. Gangopadhyay, On second order nonlinearity of cubic monomial Boolean functions., Available at: http://eprint.iacr.org/2009/502.pdf.
|
[12]
|
G. Kabatiansky and C. Tavernier, List decoding of second order Reed-Muller codes, Proceedings of the Eighteen International Symposium of Communication Theory and Applications, Ambleside, UK, 2005.
|
[13]
|
L. R. Knudsen and M. J. B. Robshaw, Non-linear approximations in linear cryptanalysis, Advances in Cryptology-Eurocrypt, Springer, Berlin, 1996, 224-236.
doi: 10.1007/3-540-68339-9_20.
|
[14]
|
G. Leander, Monomial bent functions, IEEE Transactions on Information Theory, 52 (2006), 738-743.
doi: 10.1109/TIT.2005.862121.
|
[15]
|
X. L. Li, Y. P. Hu and J. T. Gao, Lower bounds on the second order nonlinearity of Boolean functions, International Journal of Foundations of Computer Science, 22 (2011), 1331-1349.
doi: 10.1142/S012905411100874X.
|
[16]
|
R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, Cambridge, 1997.
|
[17]
|
F. J. Macwilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amesterdam, 1977.
|
[18]
|
S. Sarkar and S. Gangopadhyay, On the second order nonlinearity of a cubic Maiorana-Mcfarland bent function, Finite Fields Appl., 2009.
|
[19]
|
G. H. Sun and C. K. Wu, The lower bounds on the second order nonlinearity of three classes of Boolean functions with high nonlinearity, Information Sciences, 179 (2009), 267-278.
doi: 10.1016/j.ins.2008.10.002.
|
[20]
|
G. H. Sun and C. K. Wu, The lower bound on the second-order nonlinearity of a class of Boolean functions with high nonlinearity, Applicable Algebra in Engineering Communication and Computing, 22 (2011), 37-45.
doi: 10.1007/s00200-010-0136-y.
|
[21]
|
D. Tang, C. Carlet and X. H. Tang, On the second-order nonlinearities of some bent functions, Information Sciences, 223 (2013), 322-330.
doi: 10.1016/j.ins.2012.08.024.
|
[22]
|
D. Tang, H. D. Yan, Z. C. Zhou and X. S. Zhang, A new lower bound on the second-order nonlinearity of a class of monomial bent functions, Cryptography and Communications, 12 (2020), 77-83.
doi: 10.1007/s12095-019-00360-y.
|
[23]
|
H. D. Yan and D. Tang, Improving lower bounds on the second-order nonlinearity of three classes of Boolean functions, Discrete Mathematics, 343 (2020), 11698.
doi: 10.1016/j.disc.2019.111698.
|