A Stochastic Construction of Golay Code

我们研究给出了一种随机构造的Golay码，它是最重要的码之一，具有很高的填充密度。我们采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。通过计算机仿真，估计了获得Golay码的概率。我们的问题是从理论上计算概率。我们研究了n维球面上任意点的构形概率。我们得到了它的一个理论结果。这个结果为我们的问题迈出了第一步。Golay码的几何结构具有很高的对称性，我们的问题建议研究结晶学中对称群的统计分布。

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.