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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     author = {F. M. Malyshev and A. A. Frolov},
     title = {Classification of $(v,3)${-Configurations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {741--749},
     publisher = {mathdoc},
     volume = {91},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_5_a9/}
}
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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/