Two applications of relative difference sets: Difference triangles and negaperiodic autocorrelation functions
Two applications of relative difference sets: Difference triangles and negaperiodic autocorrelation functions
复制标题
DOI：
10.1016/j.disc.2006.06.048
复制
发表时间：
2008-07
期刊：
影响因子：
--
通讯作者：
A. Pott
中科院分区：
文献类型：
--
作者：
A. Pott
众所周知的差异集与序列及其相关属性有各种联系。本文的目的是给出（不太为人所知的）相对差值集的另外两个应用：我们使用它们来构造差值三角形（基于 A. Ling 的思想），并且我们证明半正则相对差值集的某个不存在结果意味着负周期自相关序列不存在（回答 Parker 的问题[具有低负周期自相关性的偶数长度二元序列族，见：应用代数、代数算法）和纠错码，墨尔本，2001 年，计算机科学讲义，第 2227 卷，施普林格，柏林，2001 年，第 200–209 页。]）。
The well-known difference sets have various connections with sequences and their correlation properties. It is the purpose of this note to give two more applications of the (not so well known) relative difference sets: we use them to construct difference triangles (based on an idea of A. Ling) and we show that a certain nonexistence result for semiregular relative difference sets implies the nonexistence of negaperiodic autocorrelation sequences (answering a question of Parker [Even length binary sequence families with low negaperiodic autocorrelation, in: Applied Algebra, Algebraic Algorithms and Error-correcting Codes, Melbourne, 2001, Lecture Notes in Computer Science, vol. 2227, Springer, Berlin, 2001, pp. 200–209.]).