Geodesic
Classification of $(v,3)$-Configurations
Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 741-749.

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A $(v,3)$-configuration is a nondegenerate matrix of dimension $v$ over the field $\mathrm{GF}(2)$ considered up to permutation of rows and columns and containing exactly three $1$'s in the rows and columns, while the inverse matrix has also exactly three $1$'s in the rows and columns. It is proved that, for each even $v\ge 4$, there is only one indecomposable $(v,3)$-configuration, while, for odd $v$, there are no such configurations, the only exception being the unique $(5,3)$-configuration.
Mots-clés : $(v,3)$-configuration
Keywords: nondegenerate matrix, Möbius strip. 
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F. M. Malyshev; A. A. Frolov. Classification of $(v,3)$-Configurations. Matematičeskie zametki, Tome 91 (2012) no. 5, pp. 741-749. http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a9/

[1] F. M. Malyshev, V. E. Tarakanov, “O $(v,k)$-konfiguratsiyakh”, Matem. sb., 192:9 (2001), 85–108 | MR | Zbl

[2] M. Kholl, Kombinatorika, Mir, M., 1970 | MR | Zbl

[3] A. E. Trishin, “Primery $(v,k)$-matrits”, Vestn. IKSI. Ser. «K», 2003, Spetsialnyi vypusk, posvyaschennyi 100-letiyu akademika A. N. Kolmogorova, 179–185