Matrix Codes as Ideals for Grassmannian Codes and their Weight Properties
B Hernandez, V Sison - arXiv preprint arXiv:1502.05808, 2015 - arxiv.org
B Hernandez, V Sison
arXiv preprint arXiv:1502.05808, 2015•arxiv.orgA 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 $2\times 2$ 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 …
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 $2\times 2$ 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 …
A systematic way of constructing Grassmannian codes endowed with the subspace distance as lifts of matrix codes over the prime field is introduced. The matrix codes are -subspaces of the ring of matrices over on which the rank metric is applied, and are generated as one-sided proper principal ideals by idempotent elements of . Furthermore a weight function on the non-commutative matrix ring , a power of , is studied in terms of the egalitarian and homogeneous conditions. The rank weight distribution of is completely determined by the general linear group . Finally a weight function on subspace codes is analogously defined and its egalitarian property is examined.
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