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arXiv · 2005.10887

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

Minjia Shi·Shukai Wang·Xiaoxiao Li·Denis S. Krotov
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Abstract

A frequency $n$-cube $F^n(4;2,2)$ 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 $F^4(4;2,2)$, find a testing set of size $25$ for $F^3(4;2,2)$, and derive an upper bound on the number of $F^n(4;2,2)$. Additionally, for any $n$ greater than $2$, we construct an $F^n(4;2,2)$ 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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Minjia Shi, Shukai Wang, Xiaoxiao Li, Denis S. Krotov. 2020-05-21. On the number of frequency hypercubes $F^n(4;2,2)$. https://doi.org/10.1134/s0037446621050165%2010.33048%2Fsmzh.2021.62.516

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