Connectedness of projective codes in the Grassmann graph

Abstract

Using the concept of projective systems for linear codes and elementary linear algebra, we show that projective $[n,k{]}_q$ codes form a connected subgraph in the Grassmann graph consisting of $k$-dimensional subspaces of an $n$-dimensional vector space over the $q$-element field.

There is a very simple proof of the main result which makes it obvious

References in corpus (1)

• Automorphism groups of Grassmann codes