Simplicial complexes, Demi-matroids, Flag of linear codes and pair of matroids.

Abstract

We first describe linear error-correcting codes, and show how many of their most important properties are determined by their associated matroids . We also introduce the simplicial complex of the independent sets of a matroid. We then proceed to study flags of linear codes, and recall the definition of demi-matroids, and how such demi-matroids associated to flags can describe important properties of these flags, analogous to how individual codes are described by associated matroids. We also study the interplay between demi- matroids and simplicial complexes.