$p$-matroids
Diskretnaya Matematika, Tome 17 (2005) no. 3, pp. 146-160.

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We investigate properties of $c$-matroids of the class of finitely $c$-generated semimodular lattices. This class is essentially wider than the main object of the theory of matroids, the class of geometric lattices associated with simple matroids. The $c$-matroids appear naturally in the construction of uniform codes.
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A. M. Kutyin. $p$-matroids. Diskretnaya Matematika, Tome 17 (2005) no. 3, pp. 146-160. http://geodesic.mathdoc.fr/item/DM_2005_17_3_a13/

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