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

05/21/2020

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by   Minjia Shi, et al.

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A frequency n-cube F^n(4;2,2) is an n-dimensional 4×⋯× 4 array filled by 0s and 1s such that each line contains exactly two 1s. 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