论文标题

高级平价检查盖洛伊斯戒指的代码

Low-Rank Parity-Check Codes over Galois Rings

论文作者

Renner, Julian, Neri, Alessandro, Puchinger, Sven

论文摘要

低级平价检查(LRPC)是有限场上的等级 - 尺寸代码,这是Gaborit等人提出的。 (2013)用于加密应用。受到Gabidulin代码最近对Kamche等人的某些有限环的改编的启发。 (2019年),我们在Galois环上定义和研究LRPC代码 - 一类有限的交换环。我们提供了一种基于简单的线性代码操作的解码算法,类似于Gaborit等人的解码器。我们在解码器的故障概率上得出了上限,该界限比有限磁场的情况更重要。界限仅取决于错误等级,即,独立于其自由等级。此外,我们分析了解码器的复杂性。我们获得的是,在Galois环上有一类LRPC代码,该代码可以与具有相同代码参数的Gabidulin代码分解大致相同的错误数量,但比当前最佳的Gabidulin代码解码器更快。但是,一个人需要支付的价格是一个很小的故障概率,我们可以从上面束缚。

Low-rank parity-check (LRPC) are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (2019), we define and study LRPC codes over Galois rings - a wide class of finite commutative rings. We give a decoding algorithm similar to Gaborit et al.'s decoder, based on simple linear-algebraic operations. We derive an upper bound on the failure probability of the decoder, which is significantly more involved than in the case of finite fields. The bound depends only on the rank of an error, i.e., is independent of its free rank. Further, we analyze the complexity of the decoder. We obtain that there is a class of LRPC codes over a Galois ring that can decode roughly the same number of errors as a Gabidulin code with the same code parameters, but faster than the currently best decoder for Gabidulin codes. However, the price that one needs to pay is a small failure probability, which we can bound from above.

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