Extended Boolean functions (EBFs) are one of the most important tools in cryptography and spreading sequence design in communication systems. In this paper, we use EBFs to design new sets of spreading sequences for non-orthogonal multiple access (NOMA), which is an emerging technique capable of supporting massive machine-type communications (mMTC) in 5G and beyond. In this work, first $p$-ary complementary sequences are constructed using EBFs and then, these sequences are used to design new sets of non-orthogonal spreading sequence sets having very low coherence and peak to average power ratio (PAPR). The proposed spreading sequence sets are capable of supporting a large number of active devices simultaneously. In fact, for a $p$-ary spreading sequence set, we theoretically achieve an overloading factor of $2p$, where $p$ is an odd prime. Specifically, for $p=3$, we achieve an overloading factor of $6$, which cannot be achieved through the existing constructions till date.

翻译：扩展布尔函数是密码学及通信系统扩频序列设计中最重要的工具之一。本文利用扩展布尔函数为面向第五代移动通信及未来系统的非正交多址接入技术——一种能够支持大规模机器类通信的新兴技术——设计新型扩频序列集。首先，通过扩展布尔函数构造了$p$元互补序列，进而利用这些序列设计出具有极低相干性和峰均功率比的新型非正交扩频序列集。所提出的扩频序列集能够同时支持大量活跃设备。事实上，对于$p$元扩频序列集，理论上可实现过载因子$2p$（其中$p$为奇素数）。具体而言，当$p=3$时，过载因子可达6，这一性能是现有构造方法至今无法实现的。