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Three characterizations of non-binary correlation-immune and resilient functions

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Abstract

A functionf(X 1,X 2, ...,X n ) is said to betth-order correlation-immune if the random variableZ=f(X 1,X 2,...,X n ) is independent of every set oft random variables chosen from the independent equiprobable random variablesX 1,X 2,...,X n . Additionally, if all possible outputs are equally likely, thenf is called at-resilient function. In this paper, we provide three different characterizations oft th-order correlation immune functions and resilient functions where the random variable is overGF (q). The first is in terms of the structure of a certain associated matrix. The second characterization involves Fourier transforms. The third characterization establishes the equivalence of resilient functions and large sets of orthogonal arrays.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Nebraska-Lincoln, 68588, Lincoln, NE

    K. Gopalakrishnan

  2. Department of Computer Science and Engineering and Center for Communication and Information Science, University of Nebraska-Lincoln, 68588, Lincoln, NE

    D. R. Stinson

Authors
  1. K. Gopalakrishnan
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  2. D. R. Stinson
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Gopalakrishnan, K., Stinson, D.R. Three characterizations of non-binary correlation-immune and resilient functions. Des Codes Crypt 5, 241–251 (1995). https://doi.org/10.1007/BF01388386

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  • DOI: https://doi.org/10.1007/BF01388386

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