Matrix Codes as Ideals for Grassmannian Codes and their Weight Properties [article]

Bryan Hernandez, Virgilio Sison
2015 arXiv   pre-print
A systematic way of constructing Grassmannian codes endowed with the subspace distance as lifts of matrix codes over the prime field GF(p) is introduced. The matrix codes are GF(p)-subspaces of the ring M_2(GF(p)) of 2 × 2 matrices over GF(p) on which the rank metric is applied, and are generated as one-sided proper principal ideals by idempotent elements of M_2(GF(p)). Furthermore a weight function on the non-commutative matrix ring M_2(GF(p)), q a power of p, is studied in terms of the
more » ... rian and homogeneous conditions. The rank weight distribution of M_2(GF(q)) is completely determined by the general linear group GL(2,q). Finally a weight function on subspace codes is analogously defined and its egalitarian property is examined.
arXiv:1502.05808v1 fatcat:6ci2dbbfvbfm3kp4b4ypq5uuwe