Algebraic Studies on Hadamard Matrices, Block Designs and Error-Correcting Codes

Hadamard 矩阵、分块设计和纠错码的代数研究

• 批准号: 01540086
• 负责人: ITO Noboru
• 金额: $ 0.9万
• 依托单位: Meijo University (1990)Konan University (1989)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01540086/
• 关键词: Hadamard Tournament; Even Tournament; Regular Tournament; Cyclic Tournament; Hamming Weight; Nearly Triple Regular; 3-Blocks Intersection Number; 巡回符号; 対称群; 直交ト-ナメント; 反直交ト-ナメント; 近3正則対称デザイン; 2重正則単向グラフ

(1) We have shown that there exists a regular even tournament for every positive integer v such that v is congruentto 3 modulo 8.(2) We have solved the existence problem for cyclic even tournaments. If v is congruent to 3 modulo 8, then a cyclic even tournament of order v exists if and only if 2 has a singly even order for every prime factor p of v. If v is congruent to 1 modulo 8, then a cyclic even tournament of order v exists if and only if 2 has an odd order for every prime factor p of v. In the second case an intimate relation with a binary cyclic code where the Hamming weight of every code word is a multiple of 4 exists.(3) We have determined the largest number which may be the order of the automorphism group G of a cyclic tournament of order v and the structure of G in such a case.(4) We have improved results of Alspach and Berggren concerning a tournament of order v whose automorphism group has the largest order. Namely we obtained necessary and sufficient conditions for v such that the group is a 3-group or (3, 5)-group.(5) We together with Raposa in Manila, Philippines have shown that the 3-intersection number pair is unique for a nearly triply regular symmetric design of RH-type.

(1)我们已经证明了对于每个正整数v都存在一个正则偶竞赛图，使得v与3模8全等。(2)我们解决了循环偶竞赛图的存在性问题。如果v与3模8全等，则存在阶v的循环偶竞赛当且仅当2对v的每个素因子p都具有单偶阶。如果v与1模8全等，则存在阶为v的循环偶竞赛图当且仅当对于v的每个素因子p，2具有奇阶。在第二种情况下，与二元循环码有密切关系，其中汉明每个码字的权重是4的倍数。(3)我们确定了v阶循环竞赛图的自同构群G的阶数的最大值以及在这种情况下G的结构。(4)我们改进了Alspach和Berggren关于v阶竞赛图的结果，其中v阶竞赛图的自同构群具有最大阶。即得到了v是3-群或（3，5）-群的充要条件。(5)我们与菲律宾马尼拉的Raposa一起证明了3-相交数对对于RH型的近三重正则对称设计是唯一的。

项目成果

N.Ito: "On 2ーothogonal tournaments" Discrete Mathematics(第2回グラフ理論国際会議で発表).

N.Ito：“关于 2-正交锦标赛”离散数学（在第二届国际图论会议上发表）。

N. ITO: "On cyclic tournaments" Hokkaido Mathematical J.

N. ITO：“论循环锦标赛”北海道数学杂志

N.Ito: "Subgrouks of the largest odd order of a symmetric group to appear" Proceedings of,Japan philiphine conference on graph theory and combination.

N.Ito：“出现的对称群的最大奇数阶的子群”日本菲律宾图论与组合会议论文集。

T.Taguti,H.C.Lai and S.Muroga: "Design Algorithm of Ohtimal Lages Networks by the BranchーandーBound Ahhroach" International Journal of Computer Aided VLSI Design. 1. 203-231 (1989)

T.Taguti、H.C.Lai 和 S.Muroga：“分支定界 Ahhroach 的 Ohtimal Lages 网络设计算法”国际计算机辅助 VLSI 设计杂志 1. 203-231 (1989)。

Tomoyasu Taguchi: "Agogics as a metrical rhythm and phrasing" proc.1st Intn'l conf.Music Perception and cognition(Kyoto,Japan. 219-224 (1989)

Tomoyasu Taguchi：“Agogics 作为一种韵律节奏和乐句”proc.1st Intnl conf.Music Perception and cognition（京都，日本。219-224 (1989)