Following the work of Gaborit et al. (in: The international workshop on coding and cryptography (WCC 13), 2013) defining LRPC codes over finite fields, Renner et al. (in: IEEE international symposium on information theory, ISIT 2020, 2020) defined LRPC codes over the ring of integers modulo a prime power, inspired by the paper of Kamche and Mouaha (IEEE Trans Inf Theory 65(12):7718–7735, 2019) which explored rank metric codes over finite principal ideal rings. In this work, we successfully extend the work of Renner et al. by constructing LRPC codes over the ring \(\mathbb {Z}_{m}\) which is not a chain ring. We give a decoding algorithm and we study the failure probability of the decoder.

继 Gaborit 等人的工作之后。（在：编码和密码学国际研讨会（WCC 13），2013 年）在有限域上定义 LRPC 代码，Renner 等人。（在：IEEE 信息论国际研讨会，ISIT 2020，2020）受 Kamche 和 Mouaha 的论文（IEEE Trans Inf Theory 65(12):7718–7735， 2019）探索了有限主理想环上的秩度量代码。在这项工作中，我们成功地扩展了 Renner 等人的工作。通过在不是链环的环\(\mathbb {Z}_{m}\)上构造 LRPC 代码。我们给出了一个解码算法并研究了解码器的失败概率。