The paper proposes to decode Reed-Muller (RM) codes by projecting onto only a few subspaces such that the number of projections is significantly reduced. It reveals that the probability that error pairs are canceled simultaneously in two different projections is determined by their intersection size. Then, correlation coefficient which indicates the intersection size of two subspaces in a collection is introduced for collecting subspaces. Simulation results show that our proposed approach with a small number of projections onto collected subspaces performs close to the original approach.

翻译：文件建议解码Reed-Muller(RM)代码, 方法是投射到少数子空间, 从而显著降低预测数量。 它揭示出在两种不同的预测中同时取消错误对的概率取决于它们的交叉大小。 然后, 引入相关系数, 以显示收藏中两个子空间的交叉大小 。 模拟结果显示, 我们提出的在所收集的子空间上进行少量预测的方法与最初的方法很接近 。