广西师范大学学报（自然科学版） ›› 2021, Vol. 39 ›› Issue (6): 119-129.doi: 10.16088/j.issn.1001-6600.2021040801

• 研究论文 • 上一篇    下一篇

广义Howell设计GHD(n+5,3n)的存在性

姚金洋, 胡颖, 王金华*   

  1. 南通大学 理学院, 江苏 南通 226007
  • 收稿日期:2021-04-08 修回日期:2021-05-18 出版日期:2021-11-25 发布日期:2021-12-08
  • 通讯作者: 王金华(1963—), 男, 江苏如东人, 南通大学教授, 博士。E-mail: jhwang@ntu.edu.cn
  • 基金资助:
    国家自然科学基金(11371207)

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

YAO Jinyang, HU Ying, WANG Jinhua*   

  1. School of Sciences, Nantong University, Nantong Jiangsu 226007, China
  • Received:2021-04-08 Revised:2021-05-18 Online:2021-11-25 Published:2021-12-08

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摘要： 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。

关键词: 广义Howell设计, 多层常重码, 广义Howell标架, starter-adder

Abstract: 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.

Key words: generalized Howell design, multiply constant-weight code, generalized Howell frame, starter-adder

中图分类号: 

  • O157.2
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