基于4阶分圆类的近似最佳码本的构造
Constructions of Nearly Optimal Codebooks Based on Cyclotomic Classes of Order Four
DOI: 10.12677/AAM.2019.81016, PDF,    国家自然科学基金支持
作者: 马 瑞, 亓万锋：辽宁师范大学，数学学院，辽宁 大连；唐玲丽：大连民族大学，理学院，辽宁 大连
关键词: 码本；Welch界；分圆类；几乎差集；Codebook； Welch Bound； Cyclotomic Class； Almost Difference Set
摘要: 最佳码本在许多理论与实践中有着重要的应用。但构造最佳码本相对困难。一种替代方法是构造渐进最优码本，使得当码字足够长时，构造的渐进最优码本与最优码本足够接近。本文中利用基于四阶分圆类的几乎差集构造一类新的近似最佳码本。
Abstract: Codebooks meeting the Welch bound are widely used in many research areas and applications. However, it is usually difficult to construct codebooks exactly meeting the Welch bound. A good substitute is to construct asymptotically optimal (N,K) codebooks which can approach codebooks meeting the Welch bound when N is large enough. In this paper, we construct a new class of code-book nearly meeting the Welch bound by using almost difference sets which consists of 4 order cyclotomic classes.
文章引用：马瑞, 亓万锋, 唐玲丽. 基于4阶分圆类的近似最佳码本的构造[J]. 应用数学进展, 2019, 8(1): 145-151. https://doi.org/10.12677/AAM.2019.81016

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