Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/...Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.展开更多
In case of mathematical programming problems with conflicting criteria, the Pareto set is a useful tool for a decision maker. Based on the geometric properties of the Pareto set for a bicriteria linear programming pro...In case of mathematical programming problems with conflicting criteria, the Pareto set is a useful tool for a decision maker. Based on the geometric properties of the Pareto set for a bicriteria linear programming problem, we present a simple and fast method to compute this set in the criterion space using only an elementary linear program solver. We illustrate the method by solving the pig diet formulation problem which takes into account not only the cost of the diet but also nitrogen or phosphorus excretions.展开更多
文摘Let F_qbe afinite field with q=pmelements,where pis an odd prime and mis apositive integer.Here,let D_0={(x_1,x_2)∈F_q^2\{(0,0)}:Tr(x_1^(pk1+1)+x_2^(pk2+1))=c},where c∈F_q,Tr is the trace function fromFF_qtoFpand m/(m,k_1)is odd,m/(m,k_2)is even.Define ap-ary linear code C_D =c(a_1,a_2):(a_1,a_2)∈F_q^2},where c(a_1,a_2)=(Tr(a_1x_1+a_2x_2))_((x1,x2)∈D).At most three-weight distributions of two classes of linear codes are settled.
文摘In case of mathematical programming problems with conflicting criteria, the Pareto set is a useful tool for a decision maker. Based on the geometric properties of the Pareto set for a bicriteria linear programming problem, we present a simple and fast method to compute this set in the criterion space using only an elementary linear program solver. We illustrate the method by solving the pig diet formulation problem which takes into account not only the cost of the diet but also nitrogen or phosphorus excretions.
