Abstract: With a computer-aided approach based on the connection with equitable partitions, we establish the uniqueness of the orthogonal array OA(1536,13,2,7), constructed in [D.G.Fon-Der-Flaass. Perfect 2-Colorings of a Hypercube, Sib. Math. J. 48 (2007), 740-745] as an equitable partition of the 13-cube with quotient matrix [[0,13],[3,10]]. By shortening the OA(1536,13,2,7), we obtain 3 inequivalent orthogonal arrays OA(768,12,2,6), which is a complete classification for these parameters too. After our computing, the first parameters of unclassified binary orthogonal arrays OA(N,n,2,t) attending the Friedman bound N≥2n(1−n/2(t+1)) are OA(2048,14,2,7). Such array can be obtained by puncturing any binary 1-perfect code of length 15. We construct orthogonal arrays with these and similar parameters OA(N=2n−m+1,n=2m−2,2,t=2m−1−1), m≥4, that are not punctured 1-perfect codes. Additionally, we prove that any orthogonal array OA(N,n,2,t) with even t attending the bound N≥2n(1−(n+1)/2(t+2)) induces an equitable 3-partition of the n-cube.

Cite: Krotov D.S.
On the OA(1536,13,2,7) and related orthogonal arrays
Discrete Mathematics. 2020. V.343. N2. 111659 :1-11. DOI: 10.1016/j.disc.2019.111659 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Jun 5, 2019
Accepted:	Sep 4, 2019
Published online:	Oct 20, 2019

Identifiers:

Web of science:	WOS:000504780200012
Scopus:	2-s2.0-85072512610
Elibrary:	41639578
OpenAlex:	W2974531952

Citing:

DB	Citing
Web of science	11
Scopus	12
OpenAlex	14

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