| 引用本文: | 李超.m 序列完备递归采样值的存在条件.[J].国防科技大学学报,1992,14(1):19-22.[点击复制] |
| Li Chao.Existence Condition of the Complete Recurrence Sampling Values of m-Sequences[J].Journal of National University of Defense Technology,1992,14(1):19-22[点击复制] |
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| m 序列完备递归采样值的存在条件 |
| 李超 |
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(系统工程与应用数学系)
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| 摘要: |
| 本文用群论方法讨论了n 级 m 序列完备递归采样值的存在条件，证明了对任意n级 m 序列，其完备递归采样值存在的充要条件是商群G=Zp*/H(其中p=2n - 1，Zp*={s|(s, p)=l}, H = {1,2,22，…， 2n-1)为循环群。在完备递归采样值存在的条件下，求出了完备递归采样值的个数为n,φ(φ(2n-1/n)。最后给出了递归采样值的一个重要性质。 |
| 关键词: 采样，m 序列，循环群 |
| DOI： |
| 投稿日期：1991-03-27 |
| 基金项目: |
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| Existence Condition of the Complete Recurrence Sampling Values of m-Sequences |
| Li Chao |
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(Department of System Engineering and App1ied Mathematics)
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| Abstract: |
| We discuss the existence condition for the complete recurrence sampling value of m-sequences. It is proved that for m-sequences of order n，the sufficient and necessary conditions that the complete recurrence sampling value exists are that the quotient group G=Zp*/H(p=2n - 1，Zp*={s|(s, p)= l}, H =1,2,22，…，2n-1)is cylcic group，and that the number of the complete recurrence sampling values is n?φ(φ(2n-1)/n). In the end，we give some important characteristics of the complete recurrence sampling of m-se-quences |
| Keywords: sampling,m-sequeces,cyclic group |
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