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

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。

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.