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Let $M_k$ be the (oriented) matroid of the $2^k$ points $B_k = \{-1, 1\}^k$ in $\mathbb R^k$. In other words, the (oriented) circuits of $M_k$ are the minimal (signed) linear dependences among $B_k$.

What do we know about these matroids and in particular their circuits? I'd appreciate pointers to prior work.

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A.O. Matveev's paper discusses these these matroids, but with a focus on topes rather than circuits.

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