Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear $\ell$-Intersection Pairs of Codes and Their Applications   In this paper, a linear $\ell$-intersection pair of codes is introduced as a
generalization of linear complementary pairs of codes.
  Two linear codes are said to be a linear $\ell$-intersection pair if their
intersection has dimension $\ell$.
  Characterizations and constructions of such pairs of codes are given in terms
of the corresponding generator and parity-check matrices.
  Linear $\ell$-intersection pairs of MDS codes over $\mathbb{F}_q$ of length
up to $q+1$ are given for all possible parameters.
  As an application, linear $\ell$-intersection pairs of codes are used to
construct entanglement-assisted quantum error correcting codes.
  This provides a large number of new MDS entanglement-assisted quantum error
correcting codes.

9
The categories of this paper are: nlin
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc