A {00,01,10,11}-valued function on the vertices of the n-cube is called a t-resilient (n,2)-function if it has the same number of 00s, 01s, 10s and 11s among the vertices of every subcube of dimension t. The Friedman ...
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ISBN:
(纸本)9781538692912
A {00,01,10,11}-valued function on the vertices of the n-cube is called a t-resilient (n,2)-function if it has the same number of 00s, 01s, 10s and 11s among the vertices of every subcube of dimension t. The Friedman and Fon-Der-Flaass bounds on the correlation immunity order say that such a function must satisfy t <= 2n/3 - 1;moreover, the (2n/3 - 1)-resilient (n,2)-functions correspond to the equitable partitions of the n-cube with the quotient matrix [[0, r, r, r], [r, 0, r, r], [r, r, 0, r], [r, r, r, 0]], r = n/3. We suggest constructions of such functions and corresponding partitions, show connections with Latin hypercubes and binary 1-perfect codes, characterize the non-full-rank and the reducible functions from the considered class, and discuss the possibility to make a complete characterization of the class.
This paper presents some methods for constructing new resilient functions from old ones. These methods are significant generalizations of some previously known methods. Furthermore, we construct some infinite families...
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ISBN:
(纸本)9781424439867
This paper presents some methods for constructing new resilient functions from old ones. These methods are significant generalizations of some previously known methods. Furthermore, we construct some infinite families of resilient functions with optimal nonlinearity which is particularly well-suited for combining linear feedback shift registers.
Based on the relationship between nonlinearity and resiliency of a multi-output function, we present a methodfor constructing nonintersecting linear codes from packing design. Through these linear codes, we obtain n-v...
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Based on the relationship between nonlinearity and resiliency of a multi-output function, we present a methodfor constructing nonintersecting linear codes from packing design. Through these linear codes, we obtain n-variable, m-output, t-resilient functions with very high nonlinearity. Their nonlinearities are currently the best results for most of
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