Study of algebraic coding theory via representation theory and via the theory of Groebner bases
| Project/Area Number |
26887043
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Toyota Technological Institute |
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Principal Investigator |
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| Project Period (FY) |
2014-08-29 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 代数的符号理論 / グレブナー基底 / 表現論 / 超平面配置 / 誤り訂正符号 |
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| Outline of Final Research Achievements |
The aim of this research is to apply representation theory and the theory of Groebner bases to algebraic coding theory. There is an error correcting algorithm for affine variety codes such that the theory of Groebner bases is used to determine error positions and that the discrete Fourier transform is used to determine error values. I constructed an error correcting algorithm for the projective Reed-Muller codes via the algorithm for affine variety codes. Moreover, I evaluated the number of correctable errors, the computational complexity and codeword error rates.
I also modified the discrete Fourier transform for towers of codes defined by Garcia and Stichtenoth. The computational complexity of the error correcting algorithm for codes by Garcia and Stichtenoth is reduced.
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Report
(3 results)
Research Products
(17 results)
