2002 Fiscal Year Final Research Report Summary
Theory of algebraic curves with application toward the coding theory
| Project/Area Number |
13640048
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kanagawa University |
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Principal Investigator |
HOMMA Masaaki Kanagawa Univ., Mathematics, Prof., 工学部, 教授 (80145523)
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| Co-Investigator(Kenkyū-buntansha) |
KOMEDA Jiryo Kanagawa Inst. Tech., Mathematics, Prof., 工学部, 教授 (90162065)
KATO Hiroshi Yamaguchi Univ., Mathematics, Prof., 理学部, 教授 (10016157)
ITO Hiroshi Kanagawa Univ., Mathematics, Prof., 工学部, 教授 (30168372)
OHBUCHI Akira Tokushima Univ. Mathematics, Prof., 総合科学部, 教授 (10211111)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Algebraic Curve / Special Divisor / Weierstrass pair / AG Code / Error correcting Code / Hermitian Curve |
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| Research Abstract |
The initial purpose of this research was to study algebraic curves with distinctive properties and apply its fruit to coding theory. We list the very short summaries of our harvests that the chief of the project was mainly concerned with.
1. We proposed the new invariant "the order of speciality" of a special divisor while we were studing the classical theory of Castelnuovo, and gave a classification of the curves that are extremal in the sense of the invariant.
2. We considered the two points AG-code and confirmed that its parameters are better than those of a one point code in a certain situation. Moreover we started to investigate all two points codes on a Hermitian curve, however it is still in progress.
3. We organized the international conference "Curve 02" at Yamaguchi university January 28 - 31, 2002, and then edited the proceedings.
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