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

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。

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.