Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a relatively low dimensional vector subspace of a large finite field. This particular algebraic feature can then be exploited to correct with high probability rank errors when the parameters are appropriately chosen. In this paper, we present theoretical upper-bounds on the probability that the LRPC decoding algorithm fails.

翻译：低秩奇偶校验（LRPC）码是一类秩度量纠错码，其被专门引入用于设计公钥加密方案。LRPC码基于一个校验矩阵定义，该矩阵的元素取自大有限域中一个维数相对较低的子空间。当参数选择适当时，这一特定的代数特征可用于以高概率纠正秩错误。本文提出了LRPC译码算法失败概率的理论上界。