Metzner-Kapturowski类译码器的错误码视角研究
An Error-Code Perspective on Metzner--Kapturowski-like Decoders
AI总结：
本文提出基于错误码视角的类Metzner-Kapturowski译码算法，适用于高阶交织sum-rank度量码，可纠正重量达d-2的错误，并在超出唯一译码半径时保持高成功概率，为基于码的密码系统提供新见解。
摘要：
本文研究了一种用于高阶交织sum-rank度量码的类Metzner-Kapturowski译码算法，通过错误码的概念为译码过程提供了新视角。错误码定义为构成错误矩阵的向量所张成的线性码，为译码器功能提供了更直观的理解和新见解。在交织阶足够大的前提下，该算法可纠正sum-rank重量高达d-2的错误，其中d为组成码的最小距离。该译码器适用于任意线性组成码（包括非结构化或随机码），展现了其通用性。计算复杂度为在F_{q^m}上的O(max{n^3, n^2 s})次运算，其中n为码长，s为交织阶。我们进一步研究了译码器对随机错误的成功概率，提出了一种计算该概率上界的高效算法。此外，当错误重量超过唯一译码半径时，推导了成功概率的界与近似，表明译码器在该情形下仍保持高成功概率。研究表明，该译码器可作为基于交织sum-rank度量码的密码系统设计与安全分析的有力工具。对译码过程的新见解及算法在超出唯一译码半径时的高成功概率，凸显了其在各类编码相关应用中的贡献潜力。
英文摘要：
In this paper we consider a Metzner-Kapturowski-like decoding algorithm for high-order interleaved sum-rank-metric codes, offering a novel perspective on the decoding process through the concept of an error code. The error code, defined as the linear code spanned by the vectors forming the error matrix, provides a more intuitive understanding of the decoder's functionality and new insights. The proposed algorithm can correct errors of sum-rank weight up to $d-2$, where $d$ is the minimum distance of the constituent code, given a sufficiently large interleaving order. The decoder's versatility is highlighted by its applicability to any linear constituent code, including unstructured or random codes. The computational complexity is $O(\max\{n^3, n^2 s\})$ operations over $\mathbb{F}_{q^m}$, where $n$ is the code length and $s$ is the interleaving order. We further explore the success probability of the decoder for random errors, providing an efficient algorithm to compute an upper bound on this probability. Additionally, we derive bounds and approximations for the success probability when the error weight exceeds the unique decoding radius, showing that the decoder maintains a high success probability in this regime. Our findings suggest that this decoder could be a valuable tool for the design and security analysis of code-based cryptosystems using interleaved sum-rank-metric codes. The new insights into the decoding process and the high success probability of the algorithm even beyond the unique decoding radius underscore its potential to contribute to various coding-related applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
