In this paper, we consider $ S $-chains of extremal self-dual and self-orthogonal codes and their applications in the construction of quantum codes. Then, by virtue of covering radius, we determine necessary conditions for linear codes to have subcodes with large dual distances and design a new $ S $-chain search method. As computational results, 18 $ S $-chains with large distances are obtained, and many good quantum codes can be derived from those $ S $-chains by Steane construction, some of which improve the previous results.
Citation: Chaofeng Guan, Ruihu Li, Hao Song, Liangdong Lu, Husheng Li. Ternary quantum codes constructed from extremal self-dual codes and self-orthogonal codes[J]. AIMS Mathematics, 2022, 7(4): 6516-6534. doi: 10.3934/math.2022363
In this paper, we consider $ S $-chains of extremal self-dual and self-orthogonal codes and their applications in the construction of quantum codes. Then, by virtue of covering radius, we determine necessary conditions for linear codes to have subcodes with large dual distances and design a new $ S $-chain search method. As computational results, 18 $ S $-chains with large distances are obtained, and many good quantum codes can be derived from those $ S $-chains by Steane construction, some of which improve the previous results.
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Chaofeng Guan, Ruihu Li, Hao Song, Liangdong Lu, Husheng Li. Ternary quantum codes constructed from extremal self-dual codes and self-orthogonal codes[J]. AIMS Mathematics, 2022, 7(4): 6516-6534. doi: 10.3934/math.2022363
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