2009 Fiscal Year Final Research Report
Models of encoding and decoding via Grobner basis for algebraic geometry codes and multidimensional cyclic codes
| Project/Area Number |
19760269
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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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 Toyota Technological Institute, 大学院・工学研究科, 准教授 (80329854)
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| Project Period (FY) |
2007 – 2009
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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 / エルミート曲線符号 / 代数幾何符号 / 代数曲線符号 / グレブナー基底 / 有限体 |
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| Research Abstract |
Research results are classified into three subjects as follows. 1. Searching algebraic curves that have many rational points and searching efficient codes on algebraic curves and multidimensional cyclic codes. A method to compute Grobner basis for generalized quasi-cyclic codes has been established, and thereby, a searching method for them has been established. 2. Constructing unified models of encoding and decoding system for codes on algebraic curves. 3. Application of unified system of encoding and decoding for Reed-Solomon codes. The circuit scale of the unified system for the next-generation error-correcting codes has been estimated as 40% reduction of that of the conventional system.
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