中国民航大学学报 ›› 2021, Vol. 39 ›› Issue (3): 62-64.

• 基础科学 • 上一篇    

基于有限域上仿射空间构造新码本

刘雪梅,贾丽华   

  1. (中国民航大学理学院,天津 300300) 
  • 收稿日期:2020-10-17 修回日期:2020-10-17 接受日期:2020-07-27 出版日期:2021-06-25 发布日期:2021-11-28
  • 作者简介:刘雪梅(1977—),女,黑龙江哈尔滨人,教授,硕士,研究方向为代数组合,压缩感知理论.
  • 基金资助:
    国家自然科学基金青年基金项目(11701558)

Construction of new codebook based on affine space over finite field 

LIU Xuemei, JIA Lihua   

  1. (College of Science, CAUC, Tianjin 300300, China) 
  • Received:2020-10-17 Revised:2020-10-17 Accepted:2020-07-27 Online:2021-06-25 Published:2021-11-28

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。 基于有限域上仿射空间良好的组织架构, 构造了一类新的码本, 运用仿射空间的计数定理得到码本的参数,给出了最大相关幅度达到 Welch 界的充要条件,计算了最大相关幅度渐近达到 Welch 界的条件。

关键词: 有限域, 仿射空间, 码本, Welch 界

Abstract: Codebooks are widely applied in code division multiple access systems to separate the signals of different users. Basing on the affine spaces over finite fields, a class of new codebooks are constructed. By the counting theorems of affine spaces, parameters of the codebook are obtained. Sufficient and necessary conditions for the codebooks are given to meet the Welch bound, and the conditions for the the maximum cross correlation amplitude astmptotically attains to the Welch bound are calculated.

Key words: finite field, affine space, codebook, Welch bound

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