Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate Goppa codes   In this paper, we introduce multivariate Goppa codes, which contain as a
special case the well-known, classical Goppa codes. We provide a parity check
matrix for a multivariate Goppa code in terms of a tensor product of
generalized Reed-Solomon codes. We prove that multivariate Goppa codes are
subfield subcodes of augmented Cartesian codes. By showing how this new family
of codes relates to tensor products of generalized Reed-Solomon codes and
augmented codes, we obtain information about the parameters, subcodes, duals,
and hulls of multivariate Goppa codes. We see that in certain cases, the hulls
of multivariate Goppa codes (resp., tensor product of generalized Reed-Solomon
codes), are also multivariate Goppa codes (resp. tensor product of generalized
Reed-Solomon codes). We utilize the multivariate Goppa codes to obtain
entanglement-assisted quantum error-correcting codes and to build families of
long LCD, self-dual, or self-orthogonal codes.

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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg