A new family of almost difference sets and some necessary conditions

2006 ◽  
Vol 52 (5) ◽  
pp. 2052-2061 ◽  
Author(s):  
Yuan Zhang ◽  
Jian Guo Lei ◽  
Shao Pu Zhang
Keyword(s):  
Necessary Conditions ◽  
Difference Sets ◽  
New Family ◽  
Almost Difference Sets

scholarly journals An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

scholarly journals Linear Array Thinning Exploiting Almost Difference Sets

2009 ◽  
Vol 57 (12) ◽  
pp. 3800-3812 ◽  
Author(s):  
G. Oliveri ◽  
M. Donelli ◽  
A. Massa
Keyword(s):  
Linear Array ◽  
Difference Sets ◽  
Almost Difference Sets

scholarly journals New Constructions of Asymptotically Optimal Codebooks via Cyclotomic Classes of Order 8

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Wanfeng Qi ◽  
Yueying Song ◽  
Rui Ma ◽  
Lingli Tang ◽  
Qian Wang
Keyword(s):  
Finite Fields ◽  
Difference Sets ◽  
Good Alternative ◽  
Asymptotically Optimal ◽  
Welch Bound ◽  
New Class ◽  
Almost Difference Sets

Asymptotically optimal codebooks are a family of codebooks that can approach an optimal codebook meeting the Welch bound when the lengths of codewords are large enough. They can be constructed easily and are a good alternative for optimal codebooks in many applications. In this paper, we construct a new class of asymptotically optimal codebooks by using the product of some special finite fields and almost difference sets, which are composed of cyclotomic classes of order eight.

On Some New Families of Almost Difference Sets Constructed From Cyclotomic Classes of Order 12

2016 ◽  
Vol 20 (1) ◽  
pp. 61-64
Author(s):  
Minglong Qi ◽  
Shengwu Xiong ◽  
Jingling Yuan ◽  
Wenbi Rao ◽  
Luo Zhong
Keyword(s):  
Difference Sets ◽  
Almost Difference Sets
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