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- W2914608430 abstract "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 $00$s, $01$s, $10$s and $11$s 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 $tle 2n/3-1$; 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." @default.
- W2914608430 created "2019-02-21" @default.
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- W2914608430 date "2019-01-31" @default.
- W2914608430 modified "2023-09-27" @default.
- W2914608430 title "On $(2n/3-1)$-resilient $(n,2)$-functions" @default.
- W2914608430 hasPublicationYear "2019" @default.
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