摘要
Solid码具有显著的同步和纠错能力,广泛应用于噪声信道上的信息传输.此外,solid码在同一字母表上的表示法是唯一的,在语言的纯理论研究上也发挥着至关重要的作用.本文主要研究solid码的乘积性质,推广了加拿大学者Jürgensen给出的关于两个码的乘积仍是solid码的充分条件,得到了同一字母表上的两个solid码的乘积仍然是solid码的一系列充要条件,从而深化了Jürgensen关于solid码的组合性质的工作.
Solid codes can be used in information transmission over a noisy channel because they have remarkable synchronization and error-detecting capabilities in the presence of noise in informatics.In addition,solid codes have amazing mathematical applications.They play a very important role in theoretical study of languages because of the property of unique representation for words over the same alphabet.This paper mainly studies the product properties of solid codes,and generalizes the sufficient condition given by Canadian scholar J¨urgensen that the product of two solid codes is still a solid code.A series of sufficient and necessary conditions are obtained that the product of two solid codes over the same alphabet is still a solid code,which deepens the work of J¨urgensen on the combinatorial properties of solid codes.
作者
李根全
刘海艳
王鑫
许洋洋
LI Genquan;LIU Haiyan;WANG Xin;XU Yangyang(Gansu Zhuanglang ZiJing Middle School,Pingliang 744699,China;School of Statistics and Mathematics,Yunnan University of Finance and Economics,Kunming 650000,China;School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《纯粹数学与应用数学》
2025年第4期703-713,共11页
Pure and Applied Mathematics
基金
云南省基础研究计划项目(202501AT070444)
云南省教育厅科学研究基金项目(2025J0581)。
关键词
Solid码
无重叠语言
无边字
Solid codes
non-overlapping languages
unbordered words
