北京大学学报(自然科学版)

关于几乎完美阵列的一点注记

曹喜望1,3,朱怡权2,唐翠娥3   

  1. 1北京大学数学科学学院,北京,100871;2肇庆学院,肇庆,526061;3南京航空航天大学,南京,210016
  • 收稿日期:2003-10-09 出版日期:2005-01-20 发布日期:2005-01-20

A Note on Almost Perfect Arrays

CAO Xiwang1, 3, ZHU Yiquan2, TANG Cui'e3   

  1. School of Mathematical Sciences, Peking University, Beijing, 100871, E-mail: xwcao@math.pku.edu.cn; 2Zhaoqing University, Zhaoqing, 526061; 3Nanjing University of Aeronautics and Astronautics, Nanjing, 210016
  • Received:2003-10-09 Online:2005-01-20 Published:2005-01-20

摘要: 提出了几乎完美阵列的概念,证明了完美二元阵列的存在性等价于一种特定的可分差集的存 在性。提供了一些构造完美阵列的方法。另外,关于完美阵列的存在性提出了3个猜想。

关键词: 有限域, 几乎完美阵列, 可分差集

Abstract: The conception "almost perfect arrays" is proposed and it is shown that the existence of an almost perfect binary array is equivalent to the existence of a certain divisible difference set. Some methods of constructing perfect arrays are provided. In addition, three conjectures on the existence of perfect arrays are also presented.

Key words: finite fields, almost perfect arrays, divisible difference sets

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