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线性互补对偶(LCD)码凭借其独特的结构和优异的性质，在密码学、数据存储和量子计算等多个领域均展现出显著的应用价值.因此，如何构造最优的LCD码已成为编码领域的研究热点。首先，给出了由四元[n,k ]Hermitian LCD码构造四元[n+1,k ]Hermitian LCD码的充要条件。基于这一充要条件，从对偶码理论出发，构造[n+1,k+1]Hermitian LCD码。其次，利用四元[n,k ]线性码C的HullH(C )性质，提出了三种构造最优Hermitian LCD码的方法。最后，通过删除码长的方法，利用[n,k ]Hermitian LCD码构造[n-2,k ]新的Hermitian LCD码.此外，本文还列举了一些最优的Hermitian LCD码。
Abstract：Linear complementary dual LCD codes have demonstrated significant application value in cryptography, data storage, and quantum computing due to their unique structure and excellent properties. Consequently, constructing optimal LCD codes has become a research hotspot in coding theory.This paper first establishes a necessary and sufficient condition for constructing quaternary[ n + 1,k ]Hermitian LCD codes from quaternary [ n,k ] Hermitian LCD codes. Based on this condition, we further construct[ n + 1,k + 1]Hermitian LCD codes using dual code theory. Moreover, by leveraging the properties of the HullH(C) of quaternary[ n,k ]linear codes(C), three methods for constructing optimal Hermitian LCD codes are proposed. Additionally, a new class of [ n-2,k ]Hermitian LCD codes is constructed by deleting two coordinates from existing[ n,k ]Hermitian LCD codes. Finally, several examples of optimal Hermitian LCD codes are provided.
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基本信息:
中图分类号:TN911.22
引用信息:
[1]王刚,张霞,庞彬彬.最优四元Hermitian LCD码的构造方法[J].合肥大学学报,2025,42(05):20-28.
基金信息:
合肥大学人才科研基金项目（24RC17）; 安徽省教育厅项目（2024AH051503）
2025-06-26
2025
2025-08-05
2025
1
2025-10-28
2025-10-28