Rong Luo , Bingsheng Shen , Yang Yang , Zhengchun Zhou
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引用次数: 0
Abstract
A complete complementary code (CCC) consists of M sequence sets with size M. The sum of the auto-correlation functions of each sequence set is an impulse function, and the sum of cross-correlation functions of the different sequence sets is equal to zero. Thanks to their excellent correlation, CCCs received extensive use in engineering. In addition, they are strongly connected to orthogonal matrices. In some application scenarios, additional requirements are made for CCCs, such as recently proposed for concatenative CCC (CCCC) division multiple access (CCC-CDMA) technologies. In fact, CCCCs are a special kind of CCCs which requires that each sequence set in CCC be concatenated to form a zero-correlation-zone (ZCZ) sequence set. However, this requirement is challenging, and the literature is thin since there is only one construction in this context. We propose to go beyond the literature through this contribution to reduce the gap between their interest and our limited knowledge of CCCCs. This paper will employ novel methods for designing CCCCs and precisely derive two constructions of these objects. The first is based on perfect cross Z-complementary pair and Hadamard matrices, and the second relies on extended Boolean functions. Specifically, we highlight that optimal and asymptotic optimal CCCCs could be obtained through the proposed constructions. Besides, we shall present a comparison analysis with former structures in the literature and examples to illustrate our main results.
期刊介绍：
Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering.
For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods.
The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.
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