关于<span>Z</span>_2p^m广义分圆类的一个注记

A Note on the Generalized Cyclotomic Classes of <span>Z</span>_2p^m

分圆类是有限域里经典理论,广泛应用于构造差集、设计编码等众多领域。广义分圆类是有限域上分圆类的推广。本文给出一个Z2pm广义分圆类的性质,并猜测利用若干特定组合,可以构造出Z2pm上的差集偶。

The cyclotomic class is a classic theory in finite fields, which is widely used in many fields such as constructing difference sets and encoding design. The generalized cyclotomic class is a generalization of the cyclotomic class on a finite field. This paper gives one property of cyclotomic classes of Z2pm, and proposes two conjectures about the existence of some difference set pairs consisting of a number of specific combinations of cyclotomic classes.