Error correcting codes from the viewpoints of algebraic curves and finite geometry
| Project/Area Number |
15500017
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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 |
Fundamental theory of informatics
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| Research Institution | Kanagawa University |
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Principal Investigator |
HOMMA Masaaki Kanagawa University, Faculty of Engineering, Professor, 工学部, 教授 (80145523)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Takao Yamaguchi University, Faculty of science, Professor, 理学部, 教授 (10016157)
KOMEDA Jiryo Kanagawa Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (90162065)
ISHII Naonori Nihon University, Faculty of Science and Engineering, lecturer, 理工学部, 専任講師 (10339252)
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| Project Period (FY) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Error correcting code / A Gcode / Hermitian Curve / Two-point code / Minimum distance / Positive Characteristic / 国際情報交換 / 大韓民国 / 設計距離 |
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| Research Abstract |
We studied two-point codes on the Hermitian curve y^q+y=x^<q^+> over the field F of q^2 elements, where q^2 is a power of a prime number. As the two points of those codes, we may choose the point at infinity P and the origin Q with respect to the equation. We denote by C(m, n) the code arising from the linear system L(mP+nQ).
Our problems were to compute dim C(m, n) and to find the minimum distance of C(m, n). First result is that it is enough to consider the two-point codes C(m, n) for the range 0【less than or equal】n【less than or equal】q. In the first year of this research project, we succeeded in determining the dimension of C(m, n) for all (m, n) in this range and finding the minimum distance for n=0 and q. In the second year, we happily succeeded in finding the minimum distance C(m, n) for all n with 0【less than or equal】n【less than or equal】q.
Moreover, as a corollary of the third result, we found the example of two-point code with Ω-construction in our previous paper (with S.J Kim, Goppa codes with Weierstrass pairs, Pure Appl.Algebra 162(2001)) showed the sharpness of the estimation of the minimum distance of a two-point code that explained in the previous paper.
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Report
(3 results)
Research Products
(10 results)
