Two families of nearly optimal codebooks

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• 作者：Chengju Li (1)
  Qin Yue (1)
  Yiwei Huang (2)
  
  1. Department of Mathematics ; Nanjing University of Aeronautics and Astronautics ; Nanjing ; 211100 ; People鈥檚 Republic of China
  2. School of Sciences ; China Pharmaceutical University ; Nanjing ; People鈥檚 Republic of China
  
• 关键词：Signal theory ; Difference set ; Character sums ; 94A12 ; 05B10 ; 11T24
• 刊名：Designs, Codes and Cryptography
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：75
• 期：1
• 页码：43-57
• 全文大小：199 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Coding and Information Theory
  Data Structures, Cryptology and Information Theory
  Data Encryption
  Discrete Mathematics in Computer Science
  Information, Communication and Circuits
  
• 出版者：Springer Netherlands
• ISSN：1573-7586

文摘

Codebooks are widely applied in code-division multiple-access systems. Recently, several authors constructed codebooks meeting or nearly meeting the Welch bound (i.e. nearly optimal codebooks) using difference set, almost difference set, relative difference set, and so on. In this paper, we will give two families of nearly optimal codebooks. First, we give a class of new almost difference sets and use them to construct nearly optimal codebooks. Second, we present a general construction of codebooks from partial difference sets and obtain several classes of nearly optimal codebooks.