Recently,there are extensive studies on perfect state transfer(PST for short)on graphs due to their significant applications in quantum information processing and quantum computations.However,there is not any general ...Recently,there are extensive studies on perfect state transfer(PST for short)on graphs due to their significant applications in quantum information processing and quantum computations.However,there is not any general characterization of graphs that have PST in literature.In this paper,the authors present a depiction on weighted abelian Cayley graphs having PST.They give a unified approach to describe the periodicity and the existence of PST on some specific graphs.展开更多
In this paper,we firstly construct several new kinds of Sidon spaces and Sidon sets by investigating some known results.Secondly,using these Sidon spaces,we will present a construction of cyclic subspace codes with ca...In this paper,we firstly construct several new kinds of Sidon spaces and Sidon sets by investigating some known results.Secondly,using these Sidon spaces,we will present a construction of cyclic subspace codes with cardinality τ,q^(n)-1/q-1 and minimum distance 2k-2,whereτis a positive integer.We further-more give some cyclic subspace codes with size 2τ·q^(n)-1/q-1 and without changing the minimum distance 2k-2.展开更多
Let F_(q) be a finite field and F_(q)^(s) be an extension of F_(q).Let f(x)∈F_(q)[x]be a polynomial of degree n with g c d(n,q)=1.We present a recursive formula for evaluating the exponential sum∑c∈F_(q)^(s)χ^((s)...Let F_(q) be a finite field and F_(q)^(s) be an extension of F_(q).Let f(x)∈F_(q)[x]be a polynomial of degree n with g c d(n,q)=1.We present a recursive formula for evaluating the exponential sum∑c∈F_(q)^(s)χ^((s))(f(x)).Let a and b be two elements in F_(q) with a a≠0,u be a positive integer.We obtain an estimate for the exponential sum∑c∈F^(∗)_(q)^(s)χ^((s))(ac^(u)+bc^(−1)),whereχ^((s))is the lifting of an additive characterχof F_(q).Some properties of the sequences constructed from these exponential sums are provided too.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11771007,11601003,11801007,12031011)Natural Science Foundation of Anhui Province(No.1808085MA17)。
文摘Recently,there are extensive studies on perfect state transfer(PST for short)on graphs due to their significant applications in quantum information processing and quantum computations.However,there is not any general characterization of graphs that have PST in literature.In this paper,the authors present a depiction on weighted abelian Cayley graphs having PST.They give a unified approach to describe the periodicity and the existence of PST on some specific graphs.
基金supported by the National Natural Science Foundation of China(Grant Nos.11771007,12171241).
文摘In this paper,we firstly construct several new kinds of Sidon spaces and Sidon sets by investigating some known results.Secondly,using these Sidon spaces,we will present a construction of cyclic subspace codes with cardinality τ,q^(n)-1/q-1 and minimum distance 2k-2,whereτis a positive integer.We further-more give some cyclic subspace codes with size 2τ·q^(n)-1/q-1 and without changing the minimum distance 2k-2.
文摘Let F_(q) be a finite field and F_(q)^(s) be an extension of F_(q).Let f(x)∈F_(q)[x]be a polynomial of degree n with g c d(n,q)=1.We present a recursive formula for evaluating the exponential sum∑c∈F_(q)^(s)χ^((s))(f(x)).Let a and b be two elements in F_(q) with a a≠0,u be a positive integer.We obtain an estimate for the exponential sum∑c∈F^(∗)_(q)^(s)χ^((s))(ac^(u)+bc^(−1)),whereχ^((s))is the lifting of an additive characterχof F_(q).Some properties of the sequences constructed from these exponential sums are provided too.
