Weight Distribution Properties of Rank Metric Codes And Characterization of Their Rank Weights

Abstract

In their recent paper, Hernandez et al. studied certain weight properties of rank metric codes and subspace codes. They have determined
the rank weight distribution of rank metric code M2(Fq) which is the
algebra of 2 × 2 matrices over the finite field Fq, where q is a positive
integer power of a prime. In the same work, they proved that the
rank weight is neither egalitarian nor homogeneous. In this paper,
we extended their work further to Mn(Fp) and have determined the
complete weight distribution of Mn(Fq) for n = 3. Moreover, we have
proved that for a prime p, Mn(Fp) is neither egalitarian nor homogeneous for any n, with the case n = 3 worked out seperately. Thus, we
settle this characterization problem in full generality