广义Howell设计GHD(n+5,3n)的存在性

Existence of Generalized Howell Designs GHD(n+5,3n)s

广义Howell设计是一类双可分解设计,与置换表、多层常重码有密切联系。本文利用可迁和不可迁starter-adder直接构造方法和广义Howell标架递推工具,给出广义Howell设计新的构造,除了53个可能例外值,解决了每行和每列恰好有5个空单元格的广义Howell设计GHD(n+5,3n)的存在性问题。利用广义Howell设计和多层常重码之间的关系,得到相应最优多层常重码MCWC(3,3n;1,n+5;1,n+5;8)的存在性。

Generalized Howell design is a kind of double resolvable designs,which are closely related to permutation arrays and multiply constant-weight codes.By making full use of the direct construction method of transitive starter-adder,intransitive starter-adder and generalized Howell frames as recursive tool,some new constructions for generalized Howell designs are given in this paper.The problem of existence of the generalized Howell design GHD(n+5,3n)s with exactly 5 empty cells in each row and column is solved with 53 possible exceptions.Then,the existence of the corresponding optimal multiply constant-weight codes MCWC(3,3n;1,n+5;1,n+5;8)is given by using the relationship between the generalized Howell designs and the multiply constant-weight codes.