1990 Fiscal Year Final Research Report Summary
Algebraic Studies on Hadamard Matrices, Block Designs and Error-Correcting Codes
| Project/Area Number |
01540086
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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 | Meijo University (1990)
Konan University (1989) |
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Principal Investigator |
ITO Noboru Meijo University, Department of Mathematics, Professor, 理工学部, 教授 (20151524)
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| Co-Investigator(Kenkyū-buntansha) |
FURUYA Mamoru Meijo University, Department of Mathematics, Professor, 理工学部, 教授 (80076520)
TAGUTI Tomoyasu Kokan University, Department of Applied Mathematics, Professor, 理学部, 教授 (30140388)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Hadamard Tournament / Even Tournament / Regular Tournament / Cyclic Tournament / Hamming Weight / Nearly Triple Regular / 3-Blocks Intersection Number |
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| Research Abstract |
(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.
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