2011 Fiscal Year Final Research Report
Optimal Linear Codes Problem
| Project/Area Number |
20540129
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka Prefecture University |
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Principal Investigator |
MARUTA Tatsuya 大阪府立大学, 大学院・理学系研究科, 教授 (80239152)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 線形符号 / 誤り訂正 / 最適符号 / 符号の拡張 / Griesmer限界 / 射影幾何 |
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| Research Abstract |
A linear code over the field of q elements has three important parameters : length n, dimension k and minimum distance d which indicates the ability for error correction. Such a code is called an[n, k, d]_q code. A fundamental problem in coding theory is to optimize one of the parameters n, k, d for given the other two, which is called the Optimal Linear Codes Problem. We have mainly tackled the problem to find n_q(k, d), the smallest possible length n for fixed dimension k and the minimum distance d over the field of q elements, especially for q=3, 4, 5, 8.We have obtained several new results on the problem by constructing new codes and showing the nonexistence of some linear codes attaining the known bound.
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Research Products
(22 results)
