Research on Lee Error Correcting AG Codes

Lee纠错AG码的研究

基本信息

批准号：
06805032
负责人：
SAKANIWA Kohichi
金额：
$ 0.19万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06805032/
关键词：
Multi-valued System Lee Distance Algebraic Geometric Code Extended Generalized Reed-Muller Code Extended BCH Code Fermat Curve Surface

项目摘要

This research was performed to investigate error correcting codes, especially algebraic geometric codes, for multi-valued systems where the Lee distance is preferred to the usual Hamming distance. The research results are summarized as follows :(1) The minimum Lee and Hamming distances of the extended generalized Reed-Muller codes were derived theoretically and it was clarified that in many parameters the minimum Lee distance exceeds the minimum Hamming distance.(2) Though it was thought that the algebraic geometric codes are superior to the conventional codes, it was clarified that when the number of redundant symbols is relatively small the BCH codes can be better than the algebraic geometric codes.(3) The algebraic geometric code on Fermat curve and on Fermat surface were compared and it was clarified that it is not possible to get better codes by using Fermat surface [1].(4) An improved lower bound for the dimension of subfield subcodes of algebraic geometric codes was derived [2].(5) The relationship between the BCH codes over the finite field GF (p) and the BCH codes over the finite integer ring Z_<pk> was investigated [3].References[1] Jiro Mizutani : "On the Algebraic Geometric Codes Constructed on Algebraic Surfaces, " Graduation Thesis, Tokyo Institute of Technology, Feb., 1995.[2] Ryutaroh Matsumoto : "Improved Lower Bound for the Dimension of Subfield Subcodes of Algebraic Geometric Codes, " Graduation Thesis, Tokyo Institute of Technology, Feb., 1996.[3] Shigenori Kasuya : "On the BCH Codes over the Finite Integer Ring Z_<pk>, " Graduation Thesis, Tokyo Institute of Technology, Feb., 1996.

进行了这项研究，以研究校正误差代码，尤其是代数几何代码，对于多价值系统，其中Lee距离比通常的锤距离距离。研究结果总结如下：（1）从理论上得出了扩展的广义芦苇磨牙代码的最小LEE和锤击距离，并且在许多参数中阐明了最小的LEE距离超过了最小锤距。比较了BCH代码可以比代数几何代码更好。研究了有限场GF（P）的代码和有限整数环的BCH代码Z_ <pk> [3]。参考[1] Jiro Mizutani：“在代数几何代数上建立的代数几何代码，在代数层面上建立在代数阶段，”，《毕业》，《东京》，《技术学院》，技术学院，技术，1995年，1995年，1995年，1995年。 Ryutaroh Matsumoto：“改进了代数几何代码子场尺寸的下限”，《东京理工学院毕业论文》，1996年2月。[3] Shigenori Kasuya：“关于有限整数环Z_ <pk>的BCH代码，“东京理工学院毕业论文”，1996年2月。