一类定秩集秩度量码的上界

doi:10.12677/aam.2024.1311488

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一类定秩集秩度量码的上界
New Upper Bounds of Some Rank Metric Codes with Given Ranks

DOI: 10.12677/aam.2024.1311488, PDF, 科研立项经费支持
作者: 卫烨铭, 王知庶：苏州科技大学数学科学学院，江苏苏州
关键词: 秩距离；秩度量码；常维码；Rank Distance； Rank-Metric Code； Constant Dimension Code

摘要: 常维码因其在网络编码中的重要作用受到广大学者的关注。为了构造好的常维码，Liu等人通过引入定秩集秩度量码提出了并行构造法。本文主要通过计算当q是任意素数幂时

Q_{1, 1, 1}

，

Q_{1, 2, 1}

，

Q_{2, 1, 1}

，

Q_{2, 2, 1}

的值，得到参数为

{(n \times n, 3, [1, 2])}_{q}

的定秩集秩度量码的球填充上界。

Abstract: Constant dimension codes (CDCs) have received a lot of attention due to their application in random network coding. To construct good CDCs, Liu et al. raised the parallel construction by rank metric codes with given ranks (GRMCs). This paper calculates the value of

Q_{1, 1, 1}

，

Q_{1, 2, 1}

，

Q_{2, 1, 1}

，

Q_{2, 2, 1}

when q is prime power, and the Gilbert-Hamming upper bounds of

{(n \times n, 3, [1, 2])}_{q}

GRMCs.

文章引用：卫烨铭, 王知庶. 一类定秩集秩度量码的上界[J]. 应用数学进展, 2024, 13(11): 5053-5062. https://doi.org/10.12677/aam.2024.1311488

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