The Vector Key Equation and Multisequence Shift Register Synthesis

机译：向量密钥方程和多序列移位寄存器综合

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We introduce the vector key equation for cyclic codes with more than one set of consecutive roots. Using the lattice basis reduction multisequence shift register synthesis algorithm, we find the minimal solution to the vector equation key and also give an important parameter of the multiple sequences, that is, characteristic sequence. Using it, we give a simpler sufficient and necessary condition for the uniqueness of the minimal polynomial of multiple sequences than that in [7]. The new approach enables us not only to decode cyclic codes up to HT and Roos bounds and but also to find out certain error patterns which can be decoded beyond the two bounds.

机译：我们介绍了具有多个连续根的循环码的矢量密钥方程。利用晶格基约简多序列移位寄存器综合算法，我们找到了矢量方程键的最小解，并给出了多个序列的一个重要参数，即特征序列。使用它，我们为多重序列的最小多项式的唯一性提供了一个比[7]中简单的充要条件。这种新方法不仅使我们能够解码高达HT和Roos边界的循环码，而且还能找出某些可以在两个边界之外解码的错误模式。

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《International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes(AAECC-16); 20060220-24; Las Vegas, NV(US)》|2006年|P.68-75|共8页
会议地点 Las Vegas NV(US)
作者
Li-Ping Wang;
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作者单位

Temasek Laboratories, National University of Singapore, 5 Sports Drive 2, Singapore 117508, Republic of Singapore;

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原文格式 PDF
正文语种 eng
中图分类运算器和控制器（CPU）;代数、数论、组合理论;
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专利

1. On lattice-based algebraic feedback shift registers synthesis for multisequences [J] . Li-Ping Wang, Daqing Wan Cryptography and Communications . 2018,第3期

机译：基于序列的多序列代数反馈移位寄存器合成
2. A Linear Algebraic Approach to Multisequence Shift-Register Synthesis [J] . V. R. Sidorenko, G. Schmidt Problems of information transmission . 2011,第2期

机译：多序列移位寄存器合成的线性代数方法
3. A generalization of the Berlekamp-Massey algorithm for multisequence shift-register synthesis with applications to decoding cyclic codes [J] . Feng G.-L., Tzeng K.K. IEEE Transactions on Information Theory . 1991,第5期

机译：多序列移位寄存器合成的Berlekamp-Massey算法的一般化及其在解码循环码中的应用
4. The Vector Key Equation and Multisequence Shift Register Synthesis [C] . Li-Ping Wang International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes(AAECC-16) . 2006

机译：矢量密钥方程和多音响移位寄存器合成
5. Algorithm Analysis, Code Analysis, Code Vectorization, and Code Parallelization of a Fast Finite Difference Method for Space Fractional Diffusion Equations in Three Space Dimensions. [D] . Swartz, Matthew. 2015

机译：快速有限差分方法在三个空间维度上的空间分式扩散方程的算法分析，代码分析，代码矢量化和代码并行化。
6. Vector Autoregression Structural Equation Modeling and Their Synthesis in Neuroimaging Data Analysis [O] . Gang Chen, Daniel R. Glen, Ziad S. Saad, -1

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7. On Multisequence Shift Register Synthesis and Generalized-Minimum-Distance Decoding of Reed-Solomon Codes [O] . Kamiya N. 1995

机译：Reed-Solomon码的多序列移位寄存器合成和广义最小距离解码
8. FSK (Frequency Shift Keying) Telemetry Module for Vector Measuring Current Meters [R] . Fucile, P. D., Valdes, J. R. 1987

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The Vector Key Equation and Multisequence Shift Register Synthesis

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