Modern algebraic decoding of error-correcting codes
| Project/Area Number |
23560478
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Communication/Network engineering
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| Research Institution | Toyota Technological Institute |
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Principal Investigator |
MATSUI Hajime 豊田工業大学, 工学(系)研究科(研究院), 准教授 (80329854)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
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| Keywords | 誤り訂正符号 / 離散フーリエ変換 / リード・ソロモン符号 / 代数幾何符号 / アフィン多様体符号 / p進数体 / グレブナー基底 / BCH符号 / 復号法 / p進数 |
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| Research Abstract |
1. The computational complexity of the error-value estimation in the decoding of affine variety codes has been reduced. The conventional method of the error-value estimation in the decoding of affine variety codes by Berlekamp-Massey-Sakata algorithm employs solving systems of linear equations by Gaussian elimination. In order to reduce its computational complexity, a lemma for the extension of syndrome values and discrete Fourier transforms, called Main Lemma, is established and applied to the error-value estimation. Thereby, the computational complexity third power of the code length has been reduced to the nearly second power of the code length.
2. Efficient search algorithms of high-performance generalized quasi-cyclic codes are proposed. Moreover, as an analogy of these results to the codes over rational integer rings, generalized integer codes have been newly defined, and their dual codes, search algorithms, and an enumeration method via Hecke rings have been investigated.
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Report
(4 results)
Research Products
(32 results)
