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On the number of frequency hypercubes $F^n(4;2,2)$ (2005.10887v2)

Published 21 May 2020 in math.CO and cs.DM

Abstract: A frequency $n$-cube $Fn(4;2,2)$ is an $n$-dimensional $4$-by-...-by-$4$ array filled by $0$s and $1$s such that each line contains exactly two $1$s. We classify the frequency $4$-cubes $F4(4;2,2)$, find a testing set of size $25$ for $F3(4;2,2)$, and derive an upper bound on the number of $Fn(4;2,2)$. Additionally, for any $n$ greater than $2$, we construct an $Fn(4;2,2)$ that cannot be refined to a latin hypercube, while each of its sub-$F{n-1}(4;2,2)$ can. Keywords: frequency hypercube, frequency square, latin hypercube, testing set, MDS code

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