在這篇論文中，我們提出了幾個直接由布林函數建構零和低相關
區間序列(Zero or Low Correlation Zone Sequences)的新方法。這些方
法可以直接造出所要的序列，不需要先有其他特殊的序列，而且這種
建構方法的編碼器複雜度較低。在我們的方法中，序列的長度和數
量、信號分布以及零或低相關區間的長度都可以很有彈性地調整。和
之前的建構方法相比，我們造出的序
列的零相關區間長度較長而且可以達到或接近理論值的上界。此外，我們建構
的低相關區間序列的長度是2的次方。目前為止，還沒有人提出長度2n 的
低相關區間序列的建構方法。

In this thesis, several new methods for constructing zero or low correlation zone (ZCZ or LCZ) sequence sets from the generalized Boolean functions are proposed. These methods are all direct constructions without the requirement of any special sequences or pre-search sequences and the procedures are with low complexity.
The proposed methods can freely choose the sequence length, the length of ZCZ and LCZ, the set size and the number of phases as a tradeoff.
Compared with previous methods, the length of ZCZ in our
methods is pretty large and the length of the ZCZ can be close to the theoretical bound.
Besides, the length of LCZ sequences in our method is $2^n$ and constructions for this length were not found before.

Abstract i
Contents ii
1 Introduction 1
2 Background and Denitions 4
2.1 Zero and Low Correlation Zone Sequences . . . . . . . . . . . . . . . . . . . 4
2.2 Generalized Boolean Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Generalized Reed-Muller Codes . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Further Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Related Work 13
3.1 Constructions by Special Sequences . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.1 Construction of LCZ Sequence Sets Using M-Sequences . . . . . . . . 13
3.1.2 Construction of ZCZ and LCZ Sequence Sets by Interleaving Special
Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Extension Constructions from Given LCZ Sequence Sets . . . . . . . . . . . 18
3.2.1 Method I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.2 Method II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.3 Method III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 ZCZ Sequence Sets from Generalized Boolean Functions . . . . . . . . . . . 20
4 Constructions of ZCZ Sequence Sets from Generalized Boolean Functions 25
4.1 Lemmas of Binary Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 Theorems of ZCZ Sequences from Generalized Boolean Functions . . . . . . 26
4.3 Constructions by Combining Two ZCZ Sequence Sets . . . . . . . . . . . . . 53
5 Constructions of LCZ Sequence Sets from Generalized Boolean Functions 80
5.1 Constructions of LCZ Sequence Sets by Uniting a Pair of ZCZ Sequence Sets 80
5.2 Extended Constructions of LCZ Sequence Sets . . . . . . . . . . . . . . . . . 101
5.3 Construction of ZCZ and LCZ Sequence Sets via Sequence Reordering . . . . 122
6 Conclusion 133

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