On the number of frequency hypercubes $F^n(4;2,2)$ Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2021, Volume: 62, Number: 5, Pages: 951-962 Pages count : 12 DOI: 10.1134/S0037446621050165 | ||||
| Tags | frequency hypercube, frequency square, Latin hypercube, testing set, MDS code | ||||
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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 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 every 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.
Cite:
Shi M.J.
, Wang S.K.
, Li X.X.
, Krotov D.S.
On the number of frequency hypercubes $F^n(4;2,2)$
Siberian Mathematical Journal. 2021. V.62. N5. P.951-962. DOI: 10.1134/S0037446621050165 WOS Scopus РИНЦ OpenAlex
On the number of frequency hypercubes $F^n(4;2,2)$
Siberian Mathematical Journal. 2021. V.62. N5. P.951-962. DOI: 10.1134/S0037446621050165 WOS Scopus РИНЦ OpenAlex
Original:
Ши М.
, Ван Ш.
, Ли С.
, Кротов Д.С.
О числе частотных гиперкубов Fn(4;2,2)
Сибирский математический журнал. 2021. Т.62. №5. С.1173-1187. DOI: 10.33048/smzh.2021.62.516 РИНЦ OpenAlex
О числе частотных гиперкубов Fn(4;2,2)
Сибирский математический журнал. 2021. Т.62. №5. С.1173-1187. DOI: 10.33048/smzh.2021.62.516 РИНЦ OpenAlex
Dates:
| Submitted: | Oct 20, 2020 |
| Accepted: | Jun 11, 2021 |
| Published online: | Sep 23, 2021 |
Identifiers:
| Web of science: | WOS:000698762500016 |
| Scopus: | 2-s2.0-85124958152 |
| Elibrary: | 48152076 |
| OpenAlex: | W3202504086 |