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1.
We define a dispersionless tau-symmetric bihamiltonian integrable hierarchy on the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/∞ respectively, which extends the dispersionless 2D Toda hierarchy of Takasaki and Takebe. Then we construct the deformed flat connection of the infinite-dimensional Frobenius manifold M0 introduced by Carlet, Dubrovin and Mertens (2011) [3] and, by explicitly solving the deformed flatness equations, we prove that the extended 2D Toda hierarchy coincides with principal hierarchy of M0. 相似文献
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We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows. 相似文献
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Partially-bent functions 总被引:7,自引:0,他引:7
Claude Carlet 《Designs, Codes and Cryptography》1993,3(2):135-145
We study a conjecture stated in [6] about the numbers of non-zeros of, respectively, the auto-correlation function and the Walsh transform of the function (–1)
f(x)
, wheref(x) is any boolean function on {0, 1}
n
. The result that we obtain leads us to introduce the class of partially-bent functions. We study within these functions the propagation criterion. We characterize those partially-bent functions which are balanced and prove a relation between their number (which is unknown) and the number of non-balanced partially-bent functions on {0, 1}
n–1. Eventually, we study their correlation immunity. 相似文献
6.
In a previous paper, we have obtained a characterization of the binary bent functions on (GF(2))n (n even) as linear combinations modulo
, with integral coefficients, of characteristic functions (indicators) of
-dimensional vector-subspaces of (GF(2))n. There is no uniqueness of the representation of a given bent function related to this characterization. We obtain now a new characterization for which there is uniqueness of the representation. 相似文献
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The first aim of this work was to generalize the techniques used in MacWilliams’ and Sloane’s presentation of the Kerdock
code and develop a theory of piecewise quadratic Boolean functions. This generalization led us to construct large families
of potentially new bent and almost optimal functions from quadratic forms in this piecewise fashion. We show how our motivating
example, the Kerdock code, fits into this setting. These constructions were further generalized to non-quadratic bent functions.
The resulting constructions design n-variable bent (resp. almost optimal) functions from n-variable bent or almost optimal functions.
Communicated by: T. Helleseth 相似文献
9.
CARLET Claude 《中国科学 数学(英文版)》2013,56(7):1373-1384
We study further the method of concatenating the outputs of two functions for designing an APN or a differentially 4-uniform (n, n)-function for every even n. We deduce several specific constructions of APN or differentially 4-uniform (n, n)-functions from APN and differentially 4-uniform (n/2, n/2)-functions. We also give a construction of quadratic APN functions which includes as particular cases a previous construction by the author and a more recent construction by Pott and Zhou. 相似文献
10.
We generalize to the arithmetic Walsh transform (AWT) some results which were previously known for the Walsh–Hadamard transform of Boolean functions. We first generalize the classical Poisson summation formula to the AWT. We then define a generalized notion of resilience with respect to an arbitrary statistical measure of Boolean functions. We apply the Poisson summation formula to obtain a condition equivalent to resilience for one such statistical measure. Last, we show that the AWT of a large class of Boolean functions can be expressed in terms of the AWT of a Boolean function of algebraic degree at most three in a larger number of variables. 相似文献