强差族及其在相对差族、可分组设计和光正交码中的应用  

Strong difference families and their applications in relative difference families,group divisible designs and optical orthogonal codes

作　　者：杨凯璐 王小苗 YANG Kailu;WANG Xiaomiao(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2021年第5期33-38,共6页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(11771227);浙江省自然科学基金(LY21A010005);宁波市自然科学基金(202003N4141);浙江省省属高校基本科研业务费专项资金(SJLY2020008).

摘　　要：强差族在构造其他组合设计时发挥了重要作用.本文给出了循环群上新的强差族,尤其是借助型为2的强差族获得相对差族的更好的渐近存在结果.通过分析与强差族相关的分圆条件,从渐近存在和离散例子两个角度构造了相对差族.利用计算机搜索的直接构造方法,找到阶数小于下界的相对差族.作为应用,讨论了κ∈{6,7,8,9}时区组大小为k,且组型为(κ(κ-1))^(u)的可分组设计,得到了权重为6、7、8或9的最优光正交码的无穷类.The concept of strong difference family plays an important role in constructions of other combinatorial designs.In this paper,some new strong difference families in cyclic groups are presented.In particular,strong difference families of type 2 are focused to help investigate the asymptotic existence results for relative difference families.Through applying the cyclotomic conditions attached to strong difference families,relative difference families are produced from both asymptotic existences and discrete examples.Based on the computer search,direct construction is employed to obtain a relative difference family whose order is smaller than the lower bound.As given in applications,the group divisible designs of type(κ(κ-1))^(u)with block size k are discussed forκ∈{6,7,8,9},and several classes of optimal optical orthogonal codes with weights 6,7,8 or 9 are derived.

关 键 词：强差族 相对差族 分圆类 可分组设计 光正交码 

分 类 号：O157.2[理学—数学]