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 5 G 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.

扩展布尔函数 (EBF) 是通信系统中密码学和扩展序列设计中最重要的工具之一。在本文中，我们使用 EBF 为非正交多址接入 (NOMA) 设计新的扩展序列集，这是一种新兴技术，能够支持 5G 及以后的大规模机器类型通信 (mMTC)。在这项工作中，首先使用 EBF 构建 p 元互补序列，然后使用这些序列设计新的非正交扩展序列集，这些序列集具有非常低的相干性和峰均功率比 (PAPR) 。所提出的扩展序列集能够同时支持大量有源设备。事实上，对于p-ary 扩展序列集，我们理论上实现了 2 p的过载因子，其中p是奇素数。具体来说，对于\(p=3\)，我们实现了 6 的过载因子，这是迄今为止现有结构无法实现的。