運用在資通訊的完美高斯整數序列

Perfect Gaussian Integer Sequences With Applications to Communication Systems

劉宗明(Zong-Ming Liu)

指導教授 ： 李崇道

共同指導教授 ： 陳延華(Yan-Haw Chen)

義守大學/電機資訊學院/資訊工程學系/碩士(2015年)

https://doi.org/10.6343/ISU.2015.00291

摘要

一個複數由實部和虛部組成，當實部與虛部為整數時，此複數被稱為高斯整數。一個週期長度為 n=2^m-1 的高斯整數序列，如果擁有理想的自相關特性，則被稱為完美高斯整數序列(Perfect Gaussian Integer Sequence, PGIS)；本研究目的是在分析完美高斯整數序列，利用有限體Trace表達二元序列，例如m-序列、Legendre 序列、 六次剩餘序列(Hall’s sextic residue sequence)、Gordon-Mills-Welch(GMW)、三項序列、五項序列、Welch-Gong，利用排序方法產生的二元序列，Segre hyperoval、Glynn type 1 hyperoval D(x^k) 和Glynn type 2 hyperoval D(x^(3σ+4)) ，建構出奇數長度為 n=2^m-1的完美高斯整數序列。

關鍵字

完美高斯整數序列 ； 二元序列 ； 自相關特性

並列摘要

It is well known that Gaussian integers are the complex numbers whose real and imaginary parts are both integers. There are very few studies focused on sequence design over Gaussian integers. Recent researches on the periods (lengths) of perfect Gaussian integer sequences are even numbers, prime numbers and twin-prime numbers. The aim of this research is to investigate the perfect Gaussian integer sequences of odd period n=2^m-1, where m is a positive integer. For these periods, some perfect Gaussian integer sequences are presented by the different binary sequences, such as m-sequences, Legendre sequences, Hall’s sextic residue sequences, Gordon-Mills-Welch (GMW) sequences, three-term sequences, five-term sequences, Welch-Gong sequences, Segre hyperoval sequences, Glynn type 1 hyperoval sequences as well as Glynn type 2 hyperoval sequences. The binary sequences mentioned above can be expressed as trace representations over the finite field F_(2^m ). One of the significant advantages for these obtained perfect Gaussian integer sequences is high energy efficiency with value close to one when n is a very large period.

並列關鍵字

none

參考文獻

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