Rank-metric codes as ideals for subspace codes and their weight properties

Abstract

Let , a prime, a positive integer, and the Galois field with cardinality and characteristic . In this paper, we study some weight properties of rank-metric codes and subspace codes. The rank weight is not egalitarian nor homogeneous, and the rank weight distribution of is completely determined by the general linear group . We consider subspace weight that is defined on subspace codes and examine their egalitarian property. We also present some examples of rank-metric codes endowed with the rank distance and Grassmannian codes endowed with the subspace distance. These codes were generated from left ideals of using idempotent elements of .

Keywords

• subspace codes
• grassmannian codes
• rank-metric codes