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

Fuente: arXiv
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Autori principali: Ji, Yujun, Liu, Ling, Lyu, Shanxiang, Chen, Chao, Dai, Tao, Bai, Baoming
Natura: Preprint
Pubblicazione: 2026
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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