This article is cited in 10 papers

Classification of $(v,3)$-Configurations

F. M. Malyshev, A. A. Frolov

Academy of Criptography of Russia

Abstract: 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.

Keywords: $(v,3)$-configuration, nondegenerate matrix, Möbius strip.

UDC: 519.142.1

Received: 12.11.2010

DOI: 10.4213/mzm9362

 English version: Mathematical Notes, 2012, 91:5, 689–696

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