Decoding Golay Codes and their Related Lattices: A PAC Code Perspective

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 $G^{\ast }(8,7)\mathrm{/}(8,4)$, 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 ${\mathrm{\Lambda }}_{24}$ and its principal sublattice $H_{24}$, can be also decoded efficiently.