关于构造格的自同构方法的讨论  

Discussion on the Method of Constructing Automorphism of Lattice

作　　者：冯煜晔 韩广国[1] FENG Yuye;HAN Guangguo(School of Science,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2018年第5期93-97,共5页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(11531002;11471123)

摘　　要：极值偶格等一些特定数论性质的格维数需要满足一定性质,并且其自同构群具有丰富的数学性质。为了构造出循环格的自同构群,更好地解决格中的最短向量问题,研究了48维格和72维格的自同构,在此基础上,找到它们的特殊性质。With the deepening of lattice theory,we begin to have further understanding and research on the automorphism of lattice.The lattice dimension of some special number theory is worthy of certain properties,and its automorphism is rich in mathematical properties.To find the automorphism of the lattice in some specific dimensions is one of the main research topics.By discussing whether we can construct the automorphism group of the recursive lattice,we can better solve the shortest vector problem and the nearest vector problem in the lattice.Therefore,we try to find some reasonable methods to construct the automorphism of the 48-dimensional and 72-dimensional lattice to find their special nature.

关 键 词：极值单模偶格 自同构 最小值 素数阶 

分 类 号：TN911.22[电子电信—通信与信息系统]