给出环n s(k)M上线性码的精确完全重量计数器的定义及相应的MacWilliams恒等式,并对环M n s(k)上线性码的精确完全重量计数器、k上线性码的精确重量计数器以及k上线性码的完全重量计数器之间的联系进行研究,结果表明,环M n s(k)上线性...给出环n s(k)M上线性码的精确完全重量计数器的定义及相应的MacWilliams恒等式,并对环M n s(k)上线性码的精确完全重量计数器、k上线性码的精确重量计数器以及k上线性码的完全重量计数器之间的联系进行研究,结果表明,环M n s(k)上线性码的精确完全重量计数器相比其他2种重量计数器更具一般性,可更好地用于码的结构研究和译码错误概率计算。展开更多
Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil s...Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].展开更多
Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivati...Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivatives of the second fundamental form. By use of a new maximumprinciple, some geometric properties at infinity are obtained.展开更多
The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and ap...The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications in optimal combination and linear programming fields. It can be difficultly solved by the electronic computer in exponential level time. Meanwhile in previous studies deoxyribonucleic acid （DNA） molecular operations usually were used to solve NP-complete continuous path search problems, e.g. HPP, traveling salesman problem, rarely for NP-hard problems with discrete vertices or edges solutions, such as the minimum vertex cover problem, graph coloring problem and so on. In this paper, we present a DNA algorithm for solving the MMP with DNA molecular operations. For an undirected graph with n vertices and m edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions of the MMP in proper length range using O（n^3） time. We extend the application of DNA molecular operations and simultaneously simplify the complexity of the computation.展开更多
文摘给出环n s(k)M上线性码的精确完全重量计数器的定义及相应的MacWilliams恒等式,并对环M n s(k)上线性码的精确完全重量计数器、k上线性码的精确重量计数器以及k上线性码的完全重量计数器之间的联系进行研究,结果表明,环M n s(k)上线性码的精确完全重量计数器相比其他2种重量计数器更具一般性,可更好地用于码的结构研究和译码错误概率计算。
基金supported by the Natural Science Foundation of China (No.11901062)the Sichuan Natural Science Foundation (No.2024NSFSC0417)。
文摘Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].
基金Project supported by the National Natrual Science Foundation of China (No.10271106) the Natrual Science Foundation of Zhejiang Province, China (No.102033).
文摘Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivatives of the second fundamental form. By use of a new maximumprinciple, some geometric properties at infinity are obtained.
文摘The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications in optimal combination and linear programming fields. It can be difficultly solved by the electronic computer in exponential level time. Meanwhile in previous studies deoxyribonucleic acid （DNA） molecular operations usually were used to solve NP-complete continuous path search problems, e.g. HPP, traveling salesman problem, rarely for NP-hard problems with discrete vertices or edges solutions, such as the minimum vertex cover problem, graph coloring problem and so on. In this paper, we present a DNA algorithm for solving the MMP with DNA molecular operations. For an undirected graph with n vertices and m edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions of the MMP in proper length range using O（n^3） time. We extend the application of DNA molecular operations and simultaneously simplify the complexity of the computation.
