Geodesic
$p$-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. 
@article{DM_2005_17_3_a13,
     author = {A. M. Kutyin},
     title = {$p$-matroids},
     journal = {Diskretnaya Matematika},
     pages = {146--160},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2005_17_3_a13/}
}
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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/