关于Z2pm广义分圆类的一个注记
A Note on the Generalized Cyclotomic Classes of Z2pm
DOI: 10.12677/AAM.2021.102065, PDF,    科研立项经费支持
作者: 裴孟莹, 亓万锋, 李丽彦：辽宁师范大学数学学院，辽宁 大连
关键词: 分圆类、广义分圆类、差集偶；Cyclotomic Classes； Generalized Cyclotomic Classes； Difference Set Pairs
摘要: 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。
Abstract: 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.
文章引用：裴孟莹, 亓万锋, 李丽彦. 关于Z2pm广义分圆类的一个注记[J]. 应用数学进展, 2021, 10(2): 598-602. https://doi.org/10.12677/AAM.2021.102065

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