Spaces of constant rank matrices over $GF(2)$
ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 1-5.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: For each n, we consider whether there exists an (n + 1)-dimensional space of n by n matrices over GF (2) in which each nonzero matrix has rank n - 1. Examples are given for n = 3, 4, and 5, together with evidence for the conjecture that none exist for n > 8.
Classification : 15A03, 15-04
Mots-clés : constant rank, matrices, heuristics 
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     author = {Boston, Nigel},
     title = {Spaces of constant rank matrices over $GF(2)$},
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Boston, Nigel. Spaces of constant rank matrices over $GF(2)$. ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 1-5. https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a53/