正交阵列的局部酉等价及相关线性码
Local unitary equivalence of orthogonal arrays and related linear codes
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中文总结 AI 辅助
本文通过生成矩阵构造正交阵列，建立了基于傅里叶的局部酉等价条件，并揭示了其与线性码（尤其是偶校验码）之间的显式联系，识别了由特定线性码产生的等价族。
中文摘要 AI 辅助
正交阵列（OAs）是组合配置，在实验设计、纠错码和量子信息中具有应用。局部酉（LU）等价为多体纠缠态的分类提供了自然框架。利用正交阵列与量子态之间的对应关系，Goyeneche和Życzkowski [Phys. Rev. A, 2014, 90: 022316] 提出了确定正交阵列何时为$LU$等价的问题。本文中，我们从生成矩阵构造正交阵列，并建立了基于傅里叶的$LU$等价条件，适用于正交阵列和无冗余正交阵列（IrOAs）。对于素数字母表，我们确定了所考虑的线性正交阵列的傅里叶伙伴与其对应偶校验码的阵列之间的对应关系。这给出了$LU$等价与编码理论之间的显式联系。我们还识别了由特定类别的线性码产生的$LU$等价正交阵列族。
英文摘要
Orthogonal arrays (OAs) are combinatorial configurations with applications in experimental design, error-correcting codes, and quantum information. Local unitary (LU) equivalence provides a natural framework for classifying multipartite entangled states. Using the correspondence between OAs and quantum states, Goyeneche and Życzkowski [Phys. Rev. A, 2014, 90: 022316] posed the problem of determining when OAs are $LU$ equivalent. In this paper, we construct OAs from generator matrices and establish conditions for Fourier-based $LU$ equivalence of OAs and irredundant orthogonal arrays (IrOAs). For prime alphabets, we identify the Fourier partners of the linear OAs considered here with the arrays of their corresponding dual codes. This gives an explicit connection between $LU$ equivalence and coding theory. We also identify families of $LU$ equivalent OAs arising from specific classes of linear codes.
发表机构
- Hebei Normal University（河北师范大学）
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