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| 基于有限域上奇异线性空间的码本的新构造 | |
| 引用本文： | 刘雪梅,贾丽华. 基于有限域上奇异线性空间的码本的新构造[J]. 数学的实践与认识, 2021, 0(6): 151-156 |
| 作者姓名： | 刘雪梅 贾丽华 |
| 作者单位： | 中国民航大学理学院 |
| 基金项目： | 国家自然科学基金青年基金(11701558)。 |
| 摘 要： | 码本广泛应用于码分多址系统用于区分不同用户发出的信号.基于有限域上奇异线性空间构造了一类新的码本.运用奇异线性空间的计数定理,得到了码本的参数,计算了码本的最大互相关振幅,并且给出了最大互相关振幅渐近达到Welch界的条件,证明了所构造的码本是渐近最优码本. |
| 关 键 词： | 有限域 奇异线性空间 码本 Welch界 |
New Construction of Codebooks Based on the Singular Linear Spaces Over Finite Fields |
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| LIU Xue-mei,JIA Li-hua. New Construction of Codebooks Based on the Singular Linear Spaces Over Finite Fields[J]. Mathematics in Practice and Theory, 2021, 0(6): 151-156 | |
| Authors: | LIU Xue-mei JIA Li-hua |
| Affiliation: | (College of Science,Civil Aviation University of China,Tianjin 300300,China) |
| Abstract: | Codebooks are widely applied in code division multiple access systems to separate the signals of different users.Based on the singular linear spaces over finite fields,a class of new codebooks are constructed.The parameters of the codebooks are obtained by the knowledge of Anzahl theorems of singular linear spaces.We calculate the maximum correlation amplitude of the codebooks,and give the condition that the maximum correlation amplitude asymptotically reaches to the Welch bound.Then the asymptotically optimal codebook is obtained whose restrictive conditions are looser. |
| Keywords: | finite fields singular linear spaces codebooks welch bound |
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