广义 ( n×m,{ 3,5 },1 )完美差族及相关几何正交码
Generalized ( n×m,{ 3,5 },1 ) Perfect Difference Families and Related Geometric Orthogonal Codes
DOI: 10.12677/pm.2024.147266, PDF,    国家自然科学基金支持
作者: 周丽娟：内蒙古师范大学数学科学学院，内蒙古 呼和浩特；黄月梅*：内蒙古师范大学数学科学学院，内蒙古 呼和浩特；内蒙古自治区应用数学中心，内蒙古 呼和浩特
关键词: 广义完美差族；广义完美差填充；几何正交码；半完美可分组设计；Generalized Perfect Difference Family； Generalized Perfect Difference Packing； Geometric Orthogonal Code； Semi-Perfect Group Divisible Design
摘要: DNA折纸技术在构造纳米材料中起着重要的作用。而几何正交码(GOCs)可以减少DNA折纸中宏键组的错位问题。本文通过确定(n,{3,5},1)完美差族的存在条件，并借助辅助设计与递归构造的方法，得到了广义(n×m,{3,5},1)完美差族的存在条件。又根据几何正交码与广义完美差族之间的等价关系，给出了对应的变重量的完美几何正交码的存在条件。
Abstract: DNA origami technology plays an important role in the construction of nanomaterials. Geometric Orthogonal Codes (GOCs) are used to design macro key groups in DNA origami to reduce its misalignment problems. In this paper, the existence conditions of generalized(n×m,{3,5},1)perfect difference families were determined with the aid of(n,{3,5},1)perfect difference families with auxiliary designs and recursive constructions. Then, the existence conditions of some variable-weight perfect geometric orthogonal codes were obtained from the equivalence relationship of geometric orthogonal codes and generalized perfect difference families.
文章引用：周丽娟, 黄月梅. 广义 ( n×m,{ 3,5 },1 )完美差族及相关几何正交码[J]. 理论数学, 2024, 14(7): 15-22. https://doi.org/10.12677/pm.2024.147266

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