广义Kirkman方GKS_4(n,4n)的存在性  

Existence of Generalized Kirkman Squares GKS_4(n,4n)

作　　者：吴章贵 WU Zhanggui(Fuqing Branch Of Fujian Normal University, Fuqing Fujian 350300)

机构地区：[1]福建师范大学福清分校电子与信息工程学院,福建福州350300

出　　处：《福建师大福清分校学报》2017年第5期13-15,21,共4页Journal of Fuqing Branch of Fujian Normal University

基　　金：2017年福建省中青年教师教育科研项目(项目编号:JAT170685)

摘　　要：广义Kirkman方即为Kirkman方的推广.De2a.S.A.Vanstone.在研究中发现广义Kirkman方能够构造置换阵列,而置换阵列广泛应用于电缆中的数据传输和区组密码设计等.论文主要研究s=n,k=4时的广义Kirkman方GKS_k(s,kn)的存在性问题,给出它存在的必要条件,并证明了除了5个可能的例外值外,其必要条件也是充分的.Permutation arrays are widely discussed because of their applications in data transmission over power lines.M.Deza and S.A.Vanstone pointed out that the generalized Kirkman squares is tightly connected with permutation arrays.This paper mainly discuss the existence of generalized Kirkman squares GKSk(t,kn),when t=n and k=4.We give the necessary conditions for the existence of GKSk(t,kn),and show that conditions for the existence of GKSk(s,kn)are also sufficient for t=n,k=4with some possible exceptions.

关 键 词：广义Kirkman方 拉丁方 两两正交拉丁方 

分 类 号：O157.2[理学—数学]