A Stochastic Construction of Golay Code

本文研究了Golay码的一种随机构造方法，Golay码是一种重要的高填充密度码。利用随机序列编码的方法，构造了包括Golay码在内的8个自对偶码.通过计算机模拟，估计了得到Golay码的概率.我们的问题是从理论上计算概率。研究了n维球面上任意点的构形概率。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，我们的问题提示了对晶体学对称群统计分布的研究。

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.