Year: 2015
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hernandez, Bryan, Sison, Virgilio
Institution: University of the Philippines Los Baños
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1787244719