Galois环上渐近最优码本的构造  

Constructions of asymptotically optimal codebooks over Galois rings

作　　者：徐登明[1] 孟晨 XU Dengming;MENG Chen(Sino-European Institute of Aviation Engineering,CAUC,Tianjin 300300,China;College of Science,CAUC,Tianjin 300300,China)

机构地区：[1]中国民航大学中欧航空工程师学院,天津300300 [2]中国民航大学理学院,天津300300

出　　处：《中国民航大学学报》2022年第5期59-64,共6页Journal of Civil Aviation University of China

摘　　要：具有小内积相关值的码本在很多领域具有广泛的应用。利用Galois环上高斯和与Jacobi和构造出4类码本,证得这些码本关于Welch界是渐近最优的,且码本参数是新的且灵活的。基于Galois环的性质可知在特殊情况下,这些结果可以涵盖一些有限域上的成果,使码本的研究得到新的进展。Codebooks with low value of maximum cross-correlation amplitude are widely used in many fields.Four classes of codebooks are constructed by using Gauss sums and Jacobi sums over Galois rings.It is shown that these codebooks are asymptotically optimal with respect to Welch bound,and the codebook parameters are new and flexible.Based on the properties of Galois rings,it can be seen that these results can cover some results on finite fields when special values are taken,which makes new progress in the study of codebooks.

关 键 词：GALOIS环 高斯和 JACOBI和 渐近最优码本 Welch界 

分 类 号：O157.4[理学—数学]