In this paper we generalize the notion of low-rank parity check (LRPC) codes by introducing a bilinear product over F^m q based on a generic 3-tensor in Fq^mxmxm, where Fq is the finite field with q elements. The generalized LRPC codes are Fq -linear codes in general and a particular choice of the 3-tensor corresponds to the original Fqm -linear LRPC codes. For the generalized LRPC codes, we propose two probabilistic polynomial-time decoding algorithms by adapting the decoding method for LRPC codes and also show that the proposed algorithms have a decoding failure rate similar to that of decoding LRPC codes

翻译：本文通过引入基于一般三阶张量（该张量定义于Fq^mxmxm上，其中Fq为含q个元素的有限域）的双线性积，将低秩奇偶校验（LRPC）码的概念进行了推广。广义LRPC码通常为Fq-线性码，而特定三阶张量的选取对应于原始Fqm-线性LRPC码。针对广义LRPC码，我们通过适配LRPC码的解码方法，提出了两种概率多项式时间解码算法，并证明了所提算法的解码失败率与LRPC码的解码失败率相近。