A Stochastic Construction of Golay Code

格雷码的随机构造

• 批准号: 02640194
• 负责人: ITOH Yoshiaki
• 金额: $ 0.51万
• 依托单位: The Institute of Statistical Mathematics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1990
• 资助国家: 日本
• 起止时间: 1990 至 1991
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02640194/
• 关键词: Golay Code; Self dual Code; Random packing; Symmetry; Stochastic construction; Computer simulation; Linguistic cypology; Golay符号; 自己双対符号; 幾何確率

We made research to give a stochastic construction of Golay code which is one of the most important code with very high packing density. We constructed 8 self dual codes including the Golay code, by random sequential coding. The probability of getting Golay code is estimated by computer simulation. Our problems is to calculate the probability theorestically. We studied the probability of the configuration of random points on ndimensional sphere. We obtained a theoretical result for it. The result makes the first step to our problem. The geometrical structure of the Golay code has very high symmetry, and our problem suggests the study of statistical distribution on symmetry groups for crystallography.

本文研究了高密实数码的随机构造，并给出了高密实数码的随机构造。通过随机序列编码，构造了包括Golay码在内的8个自对偶码。通过计算机仿真，估计了获得戈莱码的概率。我们的问题是从理论上计算概率。研究了n维球面上随机点构型的概率。我们得到了一个理论结果。这个结果为我们解决问题迈出了第一步。Golay码的几何结构具有很高的对称性，我们的问题建议研究晶体学中对称群的统计分布。

项目成果

Fumiyasu Komaki: "A Unified Model for Kakutani's Interval Splitting and Random Car Parking" Advances in Applied Probability.

Fumiyasu Komaki：“角谷区间分割和随机停车的统一模型”应用概率的进展。

YASUNORI FUJIKOSHI,RYOICHI SHIMIZU: "ASYMPTOTIC EXPANSIONS OF SOME DISTRIBUTIONS AND THEIR ERROR BOUNDS" Sugaku Expositions. 3. 75-96 (1990)

Yasunori Fujikoshi、Ryoichi Shimizu：“某些分布的渐近展开及其错误界限”Sugaku 阐述。

YOSHIAKI ITOH,TAKEO MATSUMOTO: "Random-Generation Model for Statistical Distribution of Point Groups" Acta Crystallographica. 47. 204-206 (1991)

YOSHIAKI ITOH、TAKEO MATSUMOTO：“点群统计分布的随机生成模型”晶体学报。

丸山 貴志子,伊藤 栄明: "ライト・フィッシャ-モデルの確率微分方程式" 統計数理. 39. 47-52 (1991)

Kishiko Maruyama、Hideaki Ito：“Wright-Fisher 模型的随机微分方程”统计数学 39. 47-52 (1991)。

Yasunori Fujikoshi: "Asympotic Expansions of some Distributions and their Error Bounds" Sugaku Expositions. 3. 75-96 (1990)

Yasunori Fujikoshi：“某些分布的渐近展开及其误差界”Sugaku 阐述。