论文标题
低级平价检查代码在整数戒指上模仿Prime Power
Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power
论文作者
论文摘要
我们在有限链环$ \ mathbb {z} _ {p^r} $的扩展环上定义和分析低级平价检查（LRPC）代码，其中$ p $是prime，$ r $是一个积极的integer。 LRPC代码最初是由Gaborit等人（2013年）就加密应用程序提出的。有限环的改编灵感来自Kamche等人最近的一篇论文。 （2019年），它通过有限的原理构建了Gabidulin代码，其中包括时空代码和网络编码的应用。我们基于简单的线性代数操作提供了一种解码算法。此外，我们在解码器的故障概率上得出了上限。上限对于等于自由等级的错误是有效的。
We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring $\mathbb{Z}_{p^r}$, where $p$ is a prime and $r$ is a positive integer. LRPC codes have originally been proposed by Gaborit et al.(2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank.
