A complete system of addition laws on an elliptic curve E is a collection of addition laws with the property that for any pair of points P1, P2 on E at least one of the addition laws in the collection can be used to compute P1＋P2. This paper proposes a complete set of the addition laws for arbitrary twisted Jacobi intersection curve.
Let q be a prime or prime power and Fq^n the extension of q elements finite field Fq with degree n （n 〉 1）. Davenport, Lenstra and School proved that there exists a primitive element α ∈ Fq^n such that α generates a normal basis of Fq^n over Fq. Later, Mullin, Gao and Lenstra, etc., raised the definition of optimal normal bases and constructed such bases. In this paper, we determine all primitive type I optimal normal bases and all finite fields in which there exists a pair of reciprocal elements α and α^-1 such that both of them generate optimal normal bases of Fq^n over Fq. Furthermore, we obtain a sufficient condition for the existence of primitive type II optimal normal bases over finite fields and prove that all primitive optimal normal elements are conjugate to each other.
The weighted graphs, where the edge weights are positive numbers, are considered. The authors obtain some lower bounds on the spectral radius and the Laplacian spectral radius of weighted graphs, and characterize the graphs for which the bounds are attained. Moreover, some known lower bounds on the spectral radius and the Laplacian spectral radius of unweighted graphs can be deduced from the bounds.
This paper presents a construction of infinite classes of binary and p-ary hyperbent functions of polynomial trace form,based on finding a zero of a Kloosterman sum.
CAO XiWang1,2,3,& HU Lei3 1Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China
