发表机构
K. J. Somaiya Institute of Technology; University of Mumbai（K. J. Somaiya理工学院; 孟买大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用Suslin在1977年基于幺模行归纳构造的矩阵，在有限域上构建了Suslin-Rao码，其码率和纠错能力优于Hamming和Simplex码，且递归构造利于高效编码，适用于实时通信。
AI 中文摘要
在1977年，A. A. Suslin在论文《关于稳定自由模》（见文献[AS]）中，为发展与Serre关于射影模问题相关的模理论时，利用幺模行归纳地构造了矩阵。我们的目标是将这些矩阵与当前应用广泛的编码理论领域联系起来。为此，我们通过考察有限域F2上的某些幺模全一向量，构造了Suslin-Rao码。与Hamming码、Simplex码和BCH码等标准码族的比较分析表明，Suslin-Rao码在码率和纠错能力方面优于Hamming码和Simplex码，尽管对于长码长，BCH码可能表现更优。误码率（BER）与信噪比（SNR）的仿真进一步支持了这些码在噪声信道中的实际适用性。构造的递归特性使得编码器设计高效，使所提出的码对实时通信系统和硬件实现具有吸引力。
英文摘要
In the year $1977,$ while developing the theory of modules arising in the context of Serre's problem on projective modules in the paper ``On Stably Free Modules" (see \cite{AS}), A. A. Suslin constructed matrices inductively using unimodular rows. Our aim is to connect these matrices to the current and applicable field of coding theory. To this end, we construct Suslin-Rao codes, by using looking at certain unimodular all one vectors over the finite field $\mathbb{F}_2$. Comparative analysis with standard families such as Hamming, Simplex and BCH codes shows that the Suslin-Rao codes achieve better performance than Hamming and Simplex codes in terms of code rate and error correction capability, though BCH codes may outperform them for large code lengths. Bit error rate (BER) versus signal-to-noise ratio (SNR) simulations further support the practical applicability of these codes in noisy channels. The recursive nature of the construction allows efficient encoder design, making the proposed codes attractive for real-time communication systems and hardware implementation.
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