In this work, we propose a decoding method of Golay codes from the perspective of Polarization Adjusted Convolutional (PAC) codes. By invoking Forney's cubing construction of Golay codes and their generators $G^*(8,7)/(8,4)$, we found different construction methods of Golay codes from PAC codes, which result in an efficient parallel list decoding algorithm with near-maximum likelihood performance. Compared with existing methods, our method can get rid of index permutation and codeword puncturing. Using the new decoding method, some related lattices, such as Leech lattice $Λ_{24}$ and its principal sublattice $H_{24}$, can be also decoded efficiently.

翻译：本文从极化调整卷积码的视角提出了一种戈莱码的解码方法。通过引入Forney的戈莱码立方构造及其生成元$G^*(8,7)/(8,4)$，我们发现了从PAC码构造戈莱码的不同方法，从而得到一种具有接近最大似然性能的高效并行列表解码算法。与现有方法相比，我们的方法能够避免索引置换和码字删余。利用这种新的解码方法，一些相关格构（如Leech格$Λ_{24}$及其主子格$H_{24}$）也能被高效解码。