New Algebraic Techniques for Constructing Sequences and Arrays with Good Correlation Properties

用于构造具有良好相关性的序列和数组的新代数技术

• 批准号: 0556191
• 负责人: Krishnasamy Arasu
• 金额: --
• 依托单位: Wright State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-10-01 至 2010-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0556191&HistoricalAwards=false
• 关键词: New; Algebraic; Techniques; Constructing; Sequences

New Algebraic Techniques for Constructing Sequences and Arrays with Good Correlation Properties K.T.ArasuDepartment of Mathematics & Statistics, Wright State University,Dayton, OH 45435 The Correlation Problem covers a broad fundamental combinatorial problem with deep mathematical content. Specific solutions to the Correlation Problem have practical diverse applications in communications, experimental design, laboratory instrumentation and manufacturing. As technology changes so too will the instances of the Correlation Problem which need solving. This research develops new mathematical techniques for attacking the problem. The Correlation Problem is to design sequences or arrays with specified dimensions with entries chosen from a specified finite set so that all non-trivial periodic autocorrelations lie in a prescribed restrictive set. Usually the autocorrelations are computed using a quadratic form. More generally, one may seek several arrays with good autocorrelations and good cross-correlations. The Correlation Problem divides into two questions: When do solutions exist, and if so, what does the solution space look like? The sequence design problems that we investigate have a variety of applications in communication engineering. The methods used will be very algebraic and would employ tools from algebra, finite fields, algebraic number theory and representation theory. Calculation of the linear span (p-ranks) of the obtained sequences will use combinatorial tools, in conjunction with the algebraic tools developed here.

用于构造具有良好相关性的序列和数组的新代数技术 K.T.Arasu 莱特州立大学数学与统计系，代顿，俄亥俄州 45435 相关性问题涵盖了具有深厚数学内容的广泛基本组合问题。 相关性问题的具体解决方案在通信、实验设计、实验室仪器和制造领域具有广泛的实际应用。 随着技术的变化，需要解决的相关性问题的实例也会发生变化。 这项研究开发了新的数学技术来解决这个问题。 相关问题是设计具有指定维度的序列或数组，其中的条目选自指定的有限集，以便所有非平凡的周期性自相关性都位于规定的限制集中。 通常，自相关是使用二次形式计算的。 更一般地，人们可以寻找具有良好自相关性和良好互相关性的多个阵列。相关性问题分为两个问题：解何时存在，如果存在，解空间是什么样的？ 我们研究的序列设计问题在通信工程中有多种应用。所使用的方法将非常代数，并且将使用代数、有限域、代数数论和表示论的工具。所获得序列的线性跨度（p 秩）的计算将使用组合工具以及此处开发的代数工具。