-
Previous Article
An extension of binary threshold sequences from Fermat quotients
- AMC Home
- This Issue
-
Next Article
Cyclic codes from two-prime generalized cyclotomic sequences of order 6
Further results on semi-bent functions in polynomial form
1. | School of Mathematical Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China, China, China |
References:
[1] |
L. Carlitz, Explicit evaluation of certain exponential sums, Math. Scand, 44 (1979), 5-16. |
[2] |
C. Carlet, Boolean Functions for Cryptography and Error Correcting Codes, in Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge Univ. Press, 2010, 257-397. |
[3] |
P. Charpin, T. Helleseth and V. Zinoviev, The divisibility modulo $24$ of Kloosterman sums of $GF(2^m)$, $m$ odd, J. Comb. Theory A, 114 (2007), 322-338.
doi: 10.1016/j.jcta.2006.06.002. |
[4] |
S. Chee, S. Lee and K. Kim, Semi-bent Functions, in Int. Conf. Theory Appl. Crypt., Springer, Berlin, 1994, 105-118. |
[5] |
J. F. Dillon and H. Dobbertin, New cyclic difference sets with Singer parameters, Finite Fields Appl., 10 (2004), 342-389.
doi: 10.1016/j.ffa.2003.09.003. |
[6] |
G. Lachaud and J. Wolfmann, The weights of the orthogonals of the extended quadratic binary Goppa codes, IEEE Trans. IT, 36 (1990), 686-692.
doi: 10.1109/18.54892. |
[7] |
R. Lidl, G. L. Mullen and G. Turnwald, Dickson Polynomials, Addison-Wesley, Reading, MA, 1993, 186-199. |
[8] |
G. Leander, Monomial bent functions, IEEE Trans. IT, 52 (2006), 738-743.
doi: 10.1109/TIT.2005.862121. |
[9] |
S. Mesnager, Bent and hyper-bent functions in polynomial form and their link with some exponential sums and Dickson polynomials, IEEE Trans. IT, 57 (2011), 5996-6009.
doi: 10.1109/TIT.2011.2124439. |
[10] |
S. Mesnager, Semi-bent functions from Dillon and Niho exponents, Kloosterman sums and Dickson polynomials, IEEE Trans. IT, 57 (2011), 7443-7458.
doi: 10.1109/TIT.2011.2160039. |
[11] |
S. Mesnager, Contributions on Boolean functions for symmetric cryptography and error correcting codes, Habilitation to Direct Research in Mathematics (HDR thesis), 2012. |
[12] |
S. Mesnager, Several new infinite families of bent functions and their duals, IEEE Trans. IT, 60 (2014), 4397-4407.
doi: 10.1109/TIT.2014.2320974. |
[13] |
S. Mesnager, On semi-bent functions and related plateaued functions over the Galois field $\mathbb F_{2^n}$, in Open Problems in Mathematics and Computational Science, Springer, 2014, 243-273. |
[14] |
S. Mesnager and J. P. Flori, Hyper-bent functions via Dillon-like exponents, IEEE Trans. IT, 59 (2013), 3215-3232.
doi: 10.1109/TIT.2013.2238580. |
[15] |
O. S. Rothaus, On bent functions, J. Combin.Theory, Ser A, 20 (1976), 300-305. |
[16] |
Y. Zheng and X. M. Zhang, Relationships between bent functions and complementary plateaued functions, in Int. Conf. Inform. Secur. Crypt., Springer, Berlin, 1999, 60-75. |
[17] |
Y. Zheng and X. M. Zhang, Plateaued functions, in Int. Conf. Inform. Commun. Secur., Springer, Berlin, 1999, 284-300.
doi: 10.1007/3-540-48892-8_22. |
show all references
References:
[1] |
L. Carlitz, Explicit evaluation of certain exponential sums, Math. Scand, 44 (1979), 5-16. |
[2] |
C. Carlet, Boolean Functions for Cryptography and Error Correcting Codes, in Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge Univ. Press, 2010, 257-397. |
[3] |
P. Charpin, T. Helleseth and V. Zinoviev, The divisibility modulo $24$ of Kloosterman sums of $GF(2^m)$, $m$ odd, J. Comb. Theory A, 114 (2007), 322-338.
doi: 10.1016/j.jcta.2006.06.002. |
[4] |
S. Chee, S. Lee and K. Kim, Semi-bent Functions, in Int. Conf. Theory Appl. Crypt., Springer, Berlin, 1994, 105-118. |
[5] |
J. F. Dillon and H. Dobbertin, New cyclic difference sets with Singer parameters, Finite Fields Appl., 10 (2004), 342-389.
doi: 10.1016/j.ffa.2003.09.003. |
[6] |
G. Lachaud and J. Wolfmann, The weights of the orthogonals of the extended quadratic binary Goppa codes, IEEE Trans. IT, 36 (1990), 686-692.
doi: 10.1109/18.54892. |
[7] |
R. Lidl, G. L. Mullen and G. Turnwald, Dickson Polynomials, Addison-Wesley, Reading, MA, 1993, 186-199. |
[8] |
G. Leander, Monomial bent functions, IEEE Trans. IT, 52 (2006), 738-743.
doi: 10.1109/TIT.2005.862121. |
[9] |
S. Mesnager, Bent and hyper-bent functions in polynomial form and their link with some exponential sums and Dickson polynomials, IEEE Trans. IT, 57 (2011), 5996-6009.
doi: 10.1109/TIT.2011.2124439. |
[10] |
S. Mesnager, Semi-bent functions from Dillon and Niho exponents, Kloosterman sums and Dickson polynomials, IEEE Trans. IT, 57 (2011), 7443-7458.
doi: 10.1109/TIT.2011.2160039. |
[11] |
S. Mesnager, Contributions on Boolean functions for symmetric cryptography and error correcting codes, Habilitation to Direct Research in Mathematics (HDR thesis), 2012. |
[12] |
S. Mesnager, Several new infinite families of bent functions and their duals, IEEE Trans. IT, 60 (2014), 4397-4407.
doi: 10.1109/TIT.2014.2320974. |
[13] |
S. Mesnager, On semi-bent functions and related plateaued functions over the Galois field $\mathbb F_{2^n}$, in Open Problems in Mathematics and Computational Science, Springer, 2014, 243-273. |
[14] |
S. Mesnager and J. P. Flori, Hyper-bent functions via Dillon-like exponents, IEEE Trans. IT, 59 (2013), 3215-3232.
doi: 10.1109/TIT.2013.2238580. |
[15] |
O. S. Rothaus, On bent functions, J. Combin.Theory, Ser A, 20 (1976), 300-305. |
[16] |
Y. Zheng and X. M. Zhang, Relationships between bent functions and complementary plateaued functions, in Int. Conf. Inform. Secur. Crypt., Springer, Berlin, 1999, 60-75. |
[17] |
Y. Zheng and X. M. Zhang, Plateaued functions, in Int. Conf. Inform. Commun. Secur., Springer, Berlin, 1999, 284-300.
doi: 10.1007/3-540-48892-8_22. |
[1] |
Gennady Bachman. Exponential sums with multiplicative coefficients. Electronic Research Announcements, 1999, 5: 128-135. |
[2] |
Sihem Mesnager, Fengrong Zhang. On constructions of bent, semi-bent and five valued spectrum functions from old bent functions. Advances in Mathematics of Communications, 2017, 11 (2) : 339-345. doi: 10.3934/amc.2017026 |
[3] |
Bimal Mandal, Aditi Kar Gangopadhyay. A note on generalization of bent boolean functions. Advances in Mathematics of Communications, 2021, 15 (2) : 329-346. doi: 10.3934/amc.2020069 |
[4] |
Dae San Kim. Infinite families of recursive formulas generating power moments of ternary Kloosterman sums with square arguments arising from symplectic groups. Advances in Mathematics of Communications, 2009, 3 (2) : 167-178. doi: 10.3934/amc.2009.3.167 |
[5] |
Tingting Pang, Nian Li, Li Zhang, Xiangyong Zeng. Several new classes of (balanced) Boolean functions with few Walsh transform values. Advances in Mathematics of Communications, 2021, 15 (4) : 757-775. doi: 10.3934/amc.2020095 |
[6] |
Dmitry Krachun, Zhi-Wei Sun. On sums of four pentagonal numbers with coefficients. Electronic Research Archive, 2020, 28 (1) : 559-566. doi: 10.3934/era.2020029 |
[7] |
Qiushuang Wang, Run Xu. A review of definitions of fractional differences and sums. Mathematical Foundations of Computing, 2022 doi: 10.3934/mfc.2022013 |
[8] |
Hai-Liang Wu, Zhi-Wei Sun. Some universal quadratic sums over the integers. Electronic Research Archive, 2019, 27: 69-87. doi: 10.3934/era.2019010 |
[9] |
Manfred Denker, Samuel Senti, Xuan Zhang. Fluctuations of ergodic sums on periodic orbits under specification. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 4665-4687. doi: 10.3934/dcds.2020197 |
[10] |
Guy Cohen, Jean-Pierre Conze. The CLT for rotated ergodic sums and related processes. Discrete and Continuous Dynamical Systems, 2013, 33 (9) : 3981-4002. doi: 10.3934/dcds.2013.33.3981 |
[11] |
Benjamin Galbally, Sergey Zelik. Cesaro summation by spheres of lattice sums and Madelung constants. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4195-4208. doi: 10.3934/cpaa.2021153 |
[12] |
Claude Carlet, Stjepan Picek. On the exponents of APN power functions and Sidon sets, sum-free sets, and Dickson polynomials. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021064 |
[13] |
Liqin Qian, Xiwang Cao. Character sums over a non-chain ring and their applications. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2020134 |
[14] |
Yinghui Dong, Guojing Wang. Ruin probability for renewal risk model with negative risk sums. Journal of Industrial and Management Optimization, 2006, 2 (2) : 229-236. doi: 10.3934/jimo.2006.2.229 |
[15] |
Vincent Astier, Thomas Unger. Signatures, sums of hermitian squares and positive cones on algebras with involution. Electronic Research Announcements, 2018, 25: 16-26. doi: 10.3934/era.2018.25.003 |
[16] |
Zhi-Wei Sun. Unification of zero-sum problems, subset sums and covers of Z. Electronic Research Announcements, 2003, 9: 51-60. |
[17] |
Guang-hui Cai. Strong laws for weighted sums of i.i.d. random variables. Electronic Research Announcements, 2006, 12: 29-36. |
[18] |
Xiao-Song Yang. Index sums of isolated singular points of positive vector fields. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 1033-1039. doi: 10.3934/dcds.2009.25.1033 |
[19] |
Barbara Brandolini, Francesco Chiacchio, Jeffrey J. Langford. Estimates for sums of eigenvalues of the free plate via the fourier transform. Communications on Pure and Applied Analysis, 2020, 19 (1) : 113-122. doi: 10.3934/cpaa.2020007 |
[20] |
Junchao Zhou, Yunge Xu, Lisha Wang, Nian Li. Nearly optimal codebooks from generalized Boolean bent functions over $ \mathbb{Z}_{4} $. Advances in Mathematics of Communications, 2022, 16 (3) : 485-501. doi: 10.3934/amc.2020121 |
2020 Impact Factor: 0.935
Tools
Metrics
Other articles
by authors
[Back to Top]