Algebraic investigation 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: 62540073
• 负责人: ITO Noboru
• 金额: $ 1.02万
• 依托单位: Konan University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1987
• 资助国家: 日本
• 起止时间: 1987 至 1988
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-62540073/
• 关键词: Hadamard Tournament; Doubly Regular Asymmetric Digraph; Automorphism Group; Difference Set; Regular Hadamard Matrix; ハミング重み; アダマール行列; ブロックデザイン; 誤り訂正符号; 有向グラフ

Ito continues to work for doubly regular asymmetric digraphs(add. DRAD). He has shown that a DRAD with rank 4 automorphism groupsis the DRAD coming from (16,6,2) kummer design, and that DRADs with rank 5 automorphism groups such that one point stabilizers have two pairs of paired orbits are the DRADs coming from difference sets of quartic residues of DF(p) where p satisfies specific donditions. Ito has introduced the concept of N-graphs for DRADs, and with it characterized DRADs, together with their spectra, coming from regular Hadamard matrices. Ito is now investigating the existence problem (strong Hadamard conjecture) of Hadamard tournament (add. HT) of order v = 4m + 3. He remarks that we have only to consider the case where m is even. Then he has found an intersting connection between HT and a specific conjugacy class C of elements of order 3 in the group of orthogonal matrices of degree v over GF(2):There exists an element in C with certain conditions if and only if there exists a HT of order v. Ito is right now occupied with this investigation on HT. Ito is receiveing stimulating advices on computer programming for HT from Taguti and on geometric structure of DRADs from Hojo.

ITO继续用于双重规则的不对称挖掘（Add。Drad）。他已经表明，一个具有4个自动形态组的drad来自（16,6,2）Kummer Design的drad，并且具有5个自动形态组的drads，因此一个点稳定器具有两对成对轨道，是来自差异的差异。 p（p）的四分之一残基，其中p满足特定的捐赠。 ITO介绍了N-Graphs的drads概念，并从普通的Hadamard矩阵中介绍了Drads以及它们的光谱。 ITO现在正在调查Hadamard Tournament（ADD。ht）的存在问题（强烈的Hadamard猜想）v = 4M + 3。他指出，我们只能考虑M甚至是M的情况。然后，他发现了HT和特定的共轭类别C的相关连接，该类别的元素3的元素元素在gf上的正交矩阵组中的元素3（2）：在C中存在一个元素，并且仅在存在时才存在某些条件。命令v。ITO的HT目前正占据了有关HT的调查。 ITO从塔古蒂（Taguti）和霍霍（Hojo）的drads几何结构进行了有关HT计算机编程的刺激建议。

项目成果

N.Ito.: Journal of Algebra. (1990)

N.Ito.：代数杂志。

M.Taguti.: International J.Computer Aided VLSI Design.

M.Taguti.：国际 J.计算机辅助 VLSI 设计。

L.M; Abatangelo; S. Dragomir; S.Hojo: "On submanifolds of Finslar spaces" in preparation.

LM；

N.Ito: Proc Singapore Gronp Theory Conference Watter de Grugeter. 151-170 (1989)

N.Ito：Proc 新加坡 Gronp 理论会议 Watter de Grugeter。

N.Itoh: Discrete Methematics. 72. 181-185 (1988)

N.Itoh：离散数学。