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- W4300485958 abstract "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 $2 times 2$ 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 egalitarian 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." @default.
- W4300485958 created "2022-10-03" @default.
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- W4300485958 date "2015-02-20" @default.
- W4300485958 modified "2023-09-26" @default.
- W4300485958 title "Matrix Codes as Ideals for Grassmannian Codes and their Weight Properties" @default.
- W4300485958 doi "https://doi.org/10.48550/arxiv.1502.05808" @default.
- W4300485958 hasPublicationYear "2015" @default.
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