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On the number of bent functions from iterative constructions: lower bounds and hypotheses
1. | Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Koptyuga 4, 630090, Novosibirsk, Russian Federation, and Novosibirsk State University, st. Pirogova 2, 630090, Novosibirsk, Russian Federation |
References:
[1] |
S. V. Agievich, On the representation of bent functions by bent rectangles, in "Proc. of the Int. Petrozavodsk Conf. on Probabilistic Methods in Discrete Mathematics,'' (2000), 121-135; preprint, arXiv:math/0502087v1 |
[2] |
A. Canteaut and P. Charpin, Decomposing bent functions, IEEE Trans. Inform. Theory, 49 (2003), 2004-2019.
doi: 10.1109/TIT.2003.814476. |
[3] |
A. Canteaut, M. Daum, H. Dobbertin and G. Leander, Finding nonnormal bent functions, Discrete Appl. Math., 154 (2006), 202-218.
doi: 10.1016/j.dam.2005.03.027. |
[4] |
C. Carlet, On bent and highly nonlinear balanced/resilient functions and their algebraic immunities, in "Applied Algebra, Algebraic Algorithms and Error Correcting Codes,'' Las Vegas, USA, (2006), 1-28. |
[5] |
C. Carlet and A. Klapper, Upper bounds on the numbers of resilient functions and of bent functions, in "Proc. of 23rd Symposium on Information Theory,'' (2002), 307-314. |
[6] |
J.-J. Climent, F. García and V. Requena, On the construction of bent functions of $n+2$ variables from bent functions of $n$ variables, Adv. Math. Commun., 2 (2008), 421-431.
doi: 10.3934/amc.2008.2.421. |
[7] |
J. F. Dillon, "Elementary Hadamard Difference Sets,'' Ph.D Thesis, University of Maryland, 1974. |
[8] |
V. E. Gmurman, "Probability Theory and Mathematical Statistics,'' Higher Educ., Moscow, 2006. |
[9] |
P. Langevin, G. Leander, Counting all bent functions in dimension eight 99270589265934370305785861242880, Des. Codes Crypt., 59 (2011), 193-205. |
[10] |
R. L. McFarland, A family of difference sets in non-cyclic groups, J. Combin. Theory Ser. A, 15 (1973), 1-10.
doi: 10.1016/0097-3165(73)90031-9. |
[11] | |
[12] |
O. Rothaus, On bent functions, J. Combin. Theory Ser. A, 20 (1976), 300-305.
doi: 10.1016/0097-3165(76)90024-8. |
[13] |
N. N. Tokareva, Automorphism group of the set of all bent functions, Discrete Math. Appl., 20 (2010), 655-664.
doi: 10.1515/DMA.2010.040. |
[14] |
N. N. Tokareva, Generalizations of bent functions. A survey, Discrete Anal. Oper. Res., 17 (2010), 34-64. |
[15] |
N. Tokareva, "Nonlinear Boolean Functions: Bent Functions and Their Generalizations,'' LAP LAMBERT Academic Publishing, Saarbrucken, Germany, 2011. |
[16] |
L. Wang and J. Zhang, A best possible computable upper bound on bent functions, J. West China, 33 (2004), 113-115. |
show all references
References:
[1] |
S. V. Agievich, On the representation of bent functions by bent rectangles, in "Proc. of the Int. Petrozavodsk Conf. on Probabilistic Methods in Discrete Mathematics,'' (2000), 121-135; preprint, arXiv:math/0502087v1 |
[2] |
A. Canteaut and P. Charpin, Decomposing bent functions, IEEE Trans. Inform. Theory, 49 (2003), 2004-2019.
doi: 10.1109/TIT.2003.814476. |
[3] |
A. Canteaut, M. Daum, H. Dobbertin and G. Leander, Finding nonnormal bent functions, Discrete Appl. Math., 154 (2006), 202-218.
doi: 10.1016/j.dam.2005.03.027. |
[4] |
C. Carlet, On bent and highly nonlinear balanced/resilient functions and their algebraic immunities, in "Applied Algebra, Algebraic Algorithms and Error Correcting Codes,'' Las Vegas, USA, (2006), 1-28. |
[5] |
C. Carlet and A. Klapper, Upper bounds on the numbers of resilient functions and of bent functions, in "Proc. of 23rd Symposium on Information Theory,'' (2002), 307-314. |
[6] |
J.-J. Climent, F. García and V. Requena, On the construction of bent functions of $n+2$ variables from bent functions of $n$ variables, Adv. Math. Commun., 2 (2008), 421-431.
doi: 10.3934/amc.2008.2.421. |
[7] |
J. F. Dillon, "Elementary Hadamard Difference Sets,'' Ph.D Thesis, University of Maryland, 1974. |
[8] |
V. E. Gmurman, "Probability Theory and Mathematical Statistics,'' Higher Educ., Moscow, 2006. |
[9] |
P. Langevin, G. Leander, Counting all bent functions in dimension eight 99270589265934370305785861242880, Des. Codes Crypt., 59 (2011), 193-205. |
[10] |
R. L. McFarland, A family of difference sets in non-cyclic groups, J. Combin. Theory Ser. A, 15 (1973), 1-10.
doi: 10.1016/0097-3165(73)90031-9. |
[11] | |
[12] |
O. Rothaus, On bent functions, J. Combin. Theory Ser. A, 20 (1976), 300-305.
doi: 10.1016/0097-3165(76)90024-8. |
[13] |
N. N. Tokareva, Automorphism group of the set of all bent functions, Discrete Math. Appl., 20 (2010), 655-664.
doi: 10.1515/DMA.2010.040. |
[14] |
N. N. Tokareva, Generalizations of bent functions. A survey, Discrete Anal. Oper. Res., 17 (2010), 34-64. |
[15] |
N. Tokareva, "Nonlinear Boolean Functions: Bent Functions and Their Generalizations,'' LAP LAMBERT Academic Publishing, Saarbrucken, Germany, 2011. |
[16] |
L. Wang and J. Zhang, A best possible computable upper bound on bent functions, J. West China, 33 (2004), 113-115. |
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