Low-rank parity-check (LRPC) code[1]
Description
An LRPC code of rank \(d\) is a rank-metric code that, when interpreted as a linear code over \(\mathbb{F}_{q^m}\), admits an \((n-k)\times n\) parity-check matrix whose entries span a subspace of \(\mathbb{F}_{q^m}\) that is at most \(d\)-dimensional.Realizations
Cryptosystem [1] that is a rank-metric analogue of NTRU [3] and MDPC [4] cryptosystems.Post-quantum cryptography [2].Cousin
- Low-density parity-check (LDPC) code— LRPC codes are rank-metric analogues of LDPC codes [1].
Member of code lists
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Parents
Low-rank parity-check (LRPC) code
References
- [1]
- P. Gaborit, G. Murat, O. Ruatta, and G. Zemor, “Low rank parity check codes and their application to cryptography”, in Proceedings of the Workshop on Coding and Cryptography WCC (2013)
- [2]
- P. Gaborit, O. Ruatta, J. Schrek, and G. Zémor, “RankSign: An Efficient Signature Algorithm Based on the Rank Metric”, Lecture Notes in Computer Science 88 (2014) DOI
- [3]
- J. Hoffstein, J. Pipher, and J. H. Silverman, “NTRU: A ring-based public key cryptosystem”, Lecture Notes in Computer Science 267 (1998) DOI
- [4]
- R. Misoczki, J.-P. Tillich, N. Sendrier, and P. S. L. M. Barreto, “MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes”, 2013 IEEE International Symposium on Information Theory 2069 (2013) DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Mazin Karjikar (2023-01-16)
- Victor V. Albert (2023-01-16)
Cite as:
“Low-rank parity-check (LRPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/lrpc, arXiv:2606.11484