Algebraic investigation on Hadamard matrices, block designs and error-correcting codes

Ito继续研究双正则非对称有向图(Add.DRAD)。他证明了具有4阶自同构群的DRAD是来自(16，6，2)Kummer设计的DRAD，具有5阶自同构群使得一个点稳定子有两对成对轨道的DRAD是来自df(P)的四次剩余的不同集的DRAD，其中p满足特定的条件。Ito引入了DRAD的N-图的概念，并用它刻画了来自正则Hadamard矩阵的DRAD及其谱。Ito现在正在研究Hadamard锦标赛(Ad.他指出，我们只需考虑m为偶数的情况。然后，他发现了HT与GF(2)上的v次正交矩阵群中的3阶元的特定共轭类C之间的有趣联系：C中存在一个元素，当且仅当存在v阶HT当且仅当存在v阶HT。伊藤正在接受来自塔古提的关于HT的计算机编程的激动人心的建议，以及来自HOJO的关于DRAD的几何结构的建议。

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.