Binary sequences constructed by Legendre symbols are widely used in communication and cryptography since they have many good pseudo-random properties.In this paper,we determine the 2-adic complexity of the sum sequenc...Binary sequences constructed by Legendre symbols are widely used in communication and cryptography since they have many good pseudo-random properties.In this paper,we determine the 2-adic complexity of the sum sequence of any k many Legendre sequences and show that the 2-adic complexity of the sum sequences of any k many Legendre sequences reaches the maximum by proving the case of k=2 and 3,which implies that the sum sequences can resist the attack of rational approximation algorithm.展开更多
In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1Cq2···Cqn,where qi(1 i n)are arbitrary positive integers.By attaching an abelian group Ai of or...In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1Cq2···Cqn,where qi(1 i n)are arbitrary positive integers.By attaching an abelian group Ai of order qi to the space Cqi(1 i n),we present the stabilizer construction of such inhomogenous quantum codes,called additive quantum codes,in term of the character theory of the abelian group A=A1⊕A2⊕···⊕An.As usual case,such construction opens a way to get inhomogenous quantum codes from the classical mixed linear codes.We also present Singleton bound for inhomogenous additive quantum codes and show several quantum codes to meet such bound by using classical mixed algebraic-geometric codes.展开更多
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.
All(2m+1)-variable symmetric Boolean functions with submaximal algebraic immunity 2m-1 are described and constructed.The total number of such Boolean functions is 32·22m-3+3m-2·24-2 for m≥2.
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
文摘Binary sequences constructed by Legendre symbols are widely used in communication and cryptography since they have many good pseudo-random properties.In this paper,we determine the 2-adic complexity of the sum sequence of any k many Legendre sequences and show that the 2-adic complexity of the sum sequences of any k many Legendre sequences reaches the maximum by proving the case of k=2 and 3,which implies that the sum sequences can resist the attack of rational approximation algorithm.
基金supported by National Natural Science Foundation of China(Grant No.10990011)
文摘In this paper,the quantum error-correcting codes are generalized to the inhomogenous quantumstate space Cq1Cq2···Cqn,where qi(1 i n)are arbitrary positive integers.By attaching an abelian group Ai of order qi to the space Cqi(1 i n),we present the stabilizer construction of such inhomogenous quantum codes,called additive quantum codes,in term of the character theory of the abelian group A=A1⊕A2⊕···⊕An.As usual case,such construction opens a way to get inhomogenous quantum codes from the classical mixed linear codes.We also present Singleton bound for inhomogenous additive quantum codes and show several quantum codes to meet such bound by using classical mixed algebraic-geometric codes.
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 by the Major State Basic Research Development Program of China(Grant No.2004CB3180004)National Natural Science Foundation of China(Grant No.60433050)
文摘All(2m+1)-variable symmetric Boolean functions with submaximal algebraic immunity 2m-1 are described and constructed.The total number of such Boolean functions is 32·22m-3+3m-2·24-2 for m≥2.
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.
