Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low-Rank Parity-Check Codes Over Finite Commutative Rings   Low-Rank Parity-Check (LRPC) codes are a class of rank metric codes that have
many applications specifically in network coding and cryptography. Recently,
LRPC codes have been extended to Galois rings which are a specific case of
finite rings. In this paper, we first define LRPC codes over finite commutative
local rings, which are bricks of finite rings, with an efficient decoder. We
improve the theoretical bound of the failure probability of the decoder. Then,
we extend the work to arbitrary finite commutative rings. Certain conditions
are generally used to ensure the success of the decoder. Over finite fields,
one of these conditions is to choose a prime number as the extension degree of
the Galois field. We have shown that one can construct LRPC codes without this
condition on the degree of Galois extension.

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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys