Difference Sets, Almost Difference Sets, and their Applications
差集、近似差集及其应用
基本信息
- 批准号:RGPIN-2015-05208
- 负责人:
- 金额:$ 0.8万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2018
- 资助国家:加拿大
- 起止时间:2018-01-01 至 2019-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The primary objective of this research program is to seek new classes of difference sets and almost difference sets, and to explore their use in a number of applications. Difference sets and almost difference sets are interesting combinatorial objects which connect number theory, combinatorics, algebra, and geometry. They have a wide range of applications in engineering, computer science, and communications. Interest in the topic increased greatly when it was discovered that the existence of a difference set over a cyclic group is equivalent to the existence of a certain type of periodic sequence with good autocorrelation properties. ***In the 1990s, advancements in the theory of difference sets began to require the use of advanced algebraic number theory. In comparison to difference sets, significantly less research has been done on the construction of almost difference sets in the past ten years. There is growing recognition of the need to conduct further research towards the construction of almost difference sets. ***Difference sets and almost difference sets have applications to a wide range of real-world problems in areas such as wireless communications, cryptography, and coding theory. In the field of wireless communications, sequences generated from difference sets have long had applications to channel coding theory for Code-Division Multiple Access (CDMA) networks. More contemporary research focuses on using sequences from difference sets to design radio access protocols which allow a massive number of devices to transmit over a shared wireless channel, in anticipation of the Internet of Things (IoT) paradigm that foresees a future with billions of wirelessly-connected devices. Difference sets and almost difference sets also have applications to stream cipher cryptography, since they are used to construct highly non-linear functions which enhance security properties such as resistance to correlation attacks. They also have many applications to coding theory, which is used for data compression and error correction.**
差集和几乎差集是联系数论、组合数学、代数和几何的有趣组合对象,它们在工程、计算机科学、数学、计算机科学和计算机科学等领域有着广泛的应用。当人们发现循环群上的差集的存在等价于具有良好自相关特性的某种类型的周期序列的存在时,对该主题的兴趣大大增加。差集理论的发展开始需要使用高级代数数论,相对于差集,近十年来几乎差集构造的研究明显较少。人们越来越认识到需要对几乎差集的构造进行进一步的研究。* 差集和几乎差集在无线通信、密码学和编码理论等领域的广泛现实问题中有应用。在无线通信领域,从差集生成的序列长期以来一直应用于码分多址(CDMA)网络的信道编码理论。更现代的研究集中在使用来自差集的序列来设计无线电接入协议,该无线电接入协议允许大量设备通过共享无线信道进行传输,以预期物联网(IoT)范例,该物联网范例预见了具有数十亿无线连接设备的未来。差集和几乎差集也可以应用于流密码加密,因为它们被用于构造高度非线性的函数,该函数增强了诸如抵抗相关攻击的安全特性。它们在编码理论中也有许多应用,编码理论用于数据压缩和纠错。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Alaca, Saban其他文献
Alaca, Saban的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Alaca, Saban', 18)}}的其他基金
Difference Sets, Almost Difference Sets, and their Applications
差集、近似差集及其应用
- 批准号:
RGPIN-2015-05208 - 财政年份:2019
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
Difference Sets, Almost Difference Sets, and their Applications
差集、近似差集及其应用
- 批准号:
RGPIN-2015-05208 - 财政年份:2017
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
Difference Sets, Almost Difference Sets, and their Applications
差集、近似差集及其应用
- 批准号:
RGPIN-2015-05208 - 财政年份:2016
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
Difference Sets, Almost Difference Sets, and their Applications
差集、近似差集及其应用
- 批准号:
RGPIN-2015-05208 - 财政年份:2015
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
Theta functions and quadratic forms, convolution sums, Lambert series and Liouville type identities and Brewer type character sums
Theta 函数和二次形式、卷积和、Lambert 级数和 Liouville 型恒等式以及 Brewer 型字符和
- 批准号:
355440-2008 - 财政年份:2012
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
Theta functions and quadratic forms, convolution sums, Lambert series and Liouville type identities and Brewer type character sums
Theta 函数和二次形式、卷积和、Lambert 级数和 Liouville 型恒等式以及 Brewer 型字符和
- 批准号:
355440-2008 - 财政年份:2011
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
Theta functions and quadratic forms, convolution sums, Lambert series and Liouville type identities and Brewer type character sums
Theta 函数和二次形式、卷积和、Lambert 级数和 Liouville 型恒等式以及 Brewer 型字符和
- 批准号:
355440-2008 - 财政年份:2010
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
Theta functions and quadratic forms, convolution sums, Lambert series and Liouville type identities and Brewer type character sums
Theta 函数和二次形式、卷积和、Lambert 级数和 Liouville 型恒等式以及 Brewer 型字符和
- 批准号:
355440-2008 - 财政年份:2009
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
Theta functions and quadratic forms, convolution sums, Lambert series and Liouville type identities and Brewer type character sums
Theta 函数和二次形式、卷积和、Lambert 级数和 Liouville 型恒等式以及 Brewer 型字符和
- 批准号:
355440-2008 - 财政年份:2008
- 资助金额:
$ 0.8万 - 项目类别:
Discovery Grants Program - Individual
相似国自然基金
基于Fuzzy Sets的视频差错掩盖技术研究
- 批准号:60672134
- 批准年份:2006
- 资助金额:25.0 万元
- 项目类别:面上项目
相似海外基金
Spatial restriction of exponential sums to thin sets and beyond
指数和对稀疏集及以上的空间限制
- 批准号:
2349828 - 财政年份:2024
- 资助金额:
$ 0.8万 - 项目类别:
Standard Grant
Research Initiation Award: Turan-type problems on partially ordered sets
研究启动奖:偏序集上的图兰型问题
- 批准号:
2247163 - 财政年份:2023
- 资助金额:
$ 0.8万 - 项目类别:
Standard Grant
New approaches for leveraging single-cell data to identify disease-critical genes and gene sets
利用单细胞数据识别疾病关键基因和基因集的新方法
- 批准号:
10768004 - 财政年份:2023
- 资助金额:
$ 0.8万 - 项目类别:
Collaborative Research: Data-Driven Invariant Sets for Provably Safe Autonomy
协作研究:数据驱动的不变集可证明安全的自治
- 批准号:
2303157 - 财政年份:2023
- 资助金额:
$ 0.8万 - 项目类别:
Standard Grant
LEAPS-MPS: Controllable sets for nonlinear switched models with applications to infectious diseases
LEAPS-MPS:非线性切换模型的可控集及其在传染病中的应用
- 批准号:
2315862 - 财政年份:2023
- 资助金额:
$ 0.8万 - 项目类别:
Standard Grant
On a Combinatorial Characterization of Dynamical Invariant Sets of Regulatory Networks
关于调节网络动态不变集的组合表征
- 批准号:
23K03240 - 财政年份:2023
- 资助金额:
$ 0.8万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Constructing large scale data sets, developing methods to analyze such data sets, and their empirical implementations
构建大规模数据集,开发分析此类数据集的方法及其实证实施
- 批准号:
23K17285 - 财政年份:2023
- 资助金额:
$ 0.8万 - 项目类别:
Grant-in-Aid for Challenging Research (Pioneering)
Investigating mechanisms of consumer reactions to promotions with brand consideration sets.
研究消费者对带有品牌考虑因素的促销活动的反应机制。
- 批准号:
23KJ0655 - 财政年份:2023
- 资助金额:
$ 0.8万 - 项目类别:
Grant-in-Aid for JSPS Fellows