1988 Fiscal Year Final Research Report Summary
Algebraic investigation on Hadamard matrices, block designs and error-correcting codes
| Project/Area Number |
62540073
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | Konan University |
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Principal Investigator |
ITO Noboru Konan University, Professor, 理学部, 教授 (20151524)
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| Co-Investigator(Kenkyū-buntansha) |
HOJO Shunichi Konan University, Professor, 理学部, 教授 (00084856)
TAGUTI Motoyasu Konan University, Professor, 理学部, 教授 (30140388)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Hadamard Tournament / Doubly Regular Asymmetric Digraph / Automorphism Group / Difference Set / Regular Hadamard Matrix / ハミング重み |
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| Research Abstract |
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.
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