Geodesic
Algebraic immunity upper bound for some Dillon's bent functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 19-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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An upper bound for the algebraic immunity of some Dillon's bent functions is obtained. It is shown that for $k = 2, 3,\ldots, 8$ the degree for Tu and Deng's function in $2^k$ variables used in the Dillon's method for constructing bent functions of the maximum algebraic immunity equals $k-1$.
Keywords: Boolean function, nonlinearity, bent function, algebraic immunity. 
@article{PDMA_2013_6_a9,
     author = {S. Y. Filyuzin},
     title = {Algebraic immunity upper bound for some {Dillon's} bent functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {19--20},
     year = {2013},
     number = {6},
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     url = {http://geodesic.mathdoc.fr/item/PDMA_2013_6_a9/}
}
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S. Y. Filyuzin. Algebraic immunity upper bound for some Dillon's bent functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 6 (2013), pp. 19-20. http://geodesic.mathdoc.fr/item/PDMA_2013_6_a9/

[1] Dillon J. F., Elementary Hadamard difference sets, Ph. D. Thesis, Univ. of Maryland, 1974 | MR

[2] Tu Z., Deng Y., “A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity”, Designs, Codes and Cryptography, 60:1 (2011), 1–14 | DOI | MR | Zbl