Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix Codes as Ideals for Grassmannian Codes and their Weight
  Properties   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.

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The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc