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AIMS Mathematics

2025, Volume 10, Issue 7: 15619-15631. doi: 10.3934/math.2025699
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Research article

Several constructions of constant dimension code using equal-division method

  • The School of Computer Science and Artificial Intelligence and Aliyun School of Big Data, Changzhou University, Changzhou 213159‌, China
  • Published: 09 July 2025

  • MSC : 11T71, 94B05

  • Constant dimension codes (CDCs) have garnered significant attention in recent years, primarily owing to their crucial applications in random network coding. A central problem in the study of CDCs involves determining the maximum achievable cardinality, denoted as $ {A_q(n, 2\delta, k)} $ for given parameters. In this paper, we propose a new approach to constructing CDCs based on the equal-division method, which we subsequently combine with existing optimal codes from prior literature. The resulting codes yield improved lower bounds for $ {A_q(n, 2\delta, k)} $ compared to previously established results across certain parameters. Furthermore, we extend our approach by incorporating multiple constructions based on distinct ways of equal division. The newly constructed CDCs have larger cardinality under some parameters.

    Citation: Yongfeng Niu, Liang Wu, Yizhuo Zhang, Huiling Yu. Several constructions of constant dimension code using equal-division method[J]. AIMS Mathematics, 2025, 10(7): 15619-15631. doi: 10.3934/math.2025699

    Related Papers:

  • Constant dimension codes (CDCs) have garnered significant attention in recent years, primarily owing to their crucial applications in random network coding. A central problem in the study of CDCs involves determining the maximum achievable cardinality, denoted as $ {A_q(n, 2\delta, k)} $ for given parameters. In this paper, we propose a new approach to constructing CDCs based on the equal-division method, which we subsequently combine with existing optimal codes from prior literature. The resulting codes yield improved lower bounds for $ {A_q(n, 2\delta, k)} $ compared to previously established results across certain parameters. Furthermore, we extend our approach by incorporating multiple constructions based on distinct ways of equal division. The newly constructed CDCs have larger cardinality under some parameters.



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