2015 Fiscal Year Final Research Report
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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| Keywords | 代数的符号理論 / グレブナー基底 / 表現論 / 超平面配置 |
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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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| Free Research Field |
代数的符号理論
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