Decoding Golay Codes and their Related Lattices: A PAC Code Perspective
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918330120536064 |
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| author | Ji, Yujun Liu, Ling Lyu, Shanxiang Chen, Chao Dai, Tao Bai, Baoming |
| author_facet | Ji, Yujun Liu, Ling Lyu, Shanxiang Chen, Chao Dai, Tao Bai, Baoming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01657 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Decoding Golay Codes and their Related Lattices: A PAC Code Perspective Ji, Yujun Liu, Ling Lyu, Shanxiang Chen, Chao Dai, Tao Bai, Baoming Information Theory 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. |
| title | Decoding Golay Codes and their Related Lattices: A PAC Code Perspective |
| topic | Information Theory |
| url | https://arxiv.org/abs/2602.01657 |