Several new series of approximately mutually unbiased bases are constructed by using Gauss sums and Jacobi sums over Galois rings GR(p2, r), and the tensor method.
In this paper a method is given to calculate the explicit expressions of embedding genus distribution for ladder type graphs and cross type graphs. As an example, we refind the genus distri- bution of the graph Jn whi...In this paper a method is given to calculate the explicit expressions of embedding genus distribution for ladder type graphs and cross type graphs. As an example, we refind the genus distri- bution of the graph Jn which is the first class of graphs studied for genus distribution where its genus depends on n.展开更多
Galois rings and exponential sums over Galois rings have many applications in algebraic combinatorics, coding theory and cryptography. In this paper, we present explicit description on the Gauss sums and Jacobi sums o...Galois rings and exponential sums over Galois rings have many applications in algebraic combinatorics, coding theory and cryptography. In this paper, we present explicit description on the Gauss sums and Jacobi sums over Galois ring GR(p2 , r), and show that the values of these sums can be reduced to the Gauss sums and Jacobi sums over finite field Fpr for all non-trivial cases.展开更多
基金supported by the Natural Science Foundation of China under Grant No.61370089the Tsinghua National Laboratory for Information Science and Technology+1 种基金by the Fundamental Research Funds for the Central Universities under Grant No.JZ2014HGBZ0349by Science and Technology on Information Assurance Lab.KJ-12-01
文摘Several new series of approximately mutually unbiased bases are constructed by using Gauss sums and Jacobi sums over Galois rings GR(p2, r), and the tensor method.
基金supported National Natural Science Foundation of China (Grant Nos. 10571013, 60433050)the State Key Development Program of Basic Research of China (Grant No. 2004CB318004)
文摘In this paper a method is given to calculate the explicit expressions of embedding genus distribution for ladder type graphs and cross type graphs. As an example, we refind the genus distri- bution of the graph Jn which is the first class of graphs studied for genus distribution where its genus depends on n.
基金supported by National Natural Science Foundation of China(Grant Nos.60973125 and 10990011)Science and Technology on Information Assurance Lab(Grant No.KJ-12-01)the Tsinghua National Lab for Information Science and Technology
文摘Galois rings and exponential sums over Galois rings have many applications in algebraic combinatorics, coding theory and cryptography. In this paper, we present explicit description on the Gauss sums and Jacobi sums over Galois ring GR(p2 , r), and show that the values of these sums can be reduced to the Gauss sums and Jacobi sums over finite field Fpr for all non-trivial cases.
