In this paper,a new class of almost binary sequence pair with a single zero element is presented.The almost binary sequence pairs with three-level correlation are constructed based on cyclotomic numbers of order 2,4,a...In this paper,a new class of almost binary sequence pair with a single zero element is presented.The almost binary sequence pairs with three-level correlation are constructed based on cyclotomic numbers of order 2,4,and 6.Most of them have good correlation and balance property,whose maximum nontrivial correlation magnitudes are 2 and the difference between the numbers of occurrence of +1's and-1's are 0 or 1.In addition,the corresponding binary sequence pairs are investigated as well and we can also get some kinds of binary sequence pairs with optimum balance and good correlation.展开更多
In this paper, explicit determination of the cyclotomic numbers of order l and 2l, for odd prime l ≡ 3 (mod 4), over finite field Fq in the index 2 case are obtained, utilizing the explicit formulas on the correspond...In this paper, explicit determination of the cyclotomic numbers of order l and 2l, for odd prime l ≡ 3 (mod 4), over finite field Fq in the index 2 case are obtained, utilizing the explicit formulas on the corresponding Gauss sums. The main results in this paper are related with the number of rational points of certain elliptic curve, called "Legendre curve", and the properties and value distribution of such number are also presented.展开更多
A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic numbers.Then,the authors determine explicitly thecomplexity of such normal bases an...A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic numbers.Then,the authors determine explicitly thecomplexity of such normal bases and their dual bases in several cases where the related cyclotomicnumbers have been calculated.Particularly,the authors find several series of such normal bases withlow complexity.展开更多
基金Supported by the National Natural Science Foundation of China (No. 60872061,60971126,and 61172094)
文摘In this paper,a new class of almost binary sequence pair with a single zero element is presented.The almost binary sequence pairs with three-level correlation are constructed based on cyclotomic numbers of order 2,4,and 6.Most of them have good correlation and balance property,whose maximum nontrivial correlation magnitudes are 2 and the difference between the numbers of occurrence of +1's and-1's are 0 or 1.In addition,the corresponding binary sequence pairs are investigated as well and we can also get some kinds of binary sequence pairs with optimum balance and good correlation.
基金supported by National Natural Science Foundation of China(Grant Nos.10990011,11001145 and 61170289)the Science and Technology on Information Assurance Laboratory Foundation(Grant No.KJ-12-01)
文摘In this paper, explicit determination of the cyclotomic numbers of order l and 2l, for odd prime l ≡ 3 (mod 4), over finite field Fq in the index 2 case are obtained, utilizing the explicit formulas on the corresponding Gauss sums. The main results in this paper are related with the number of rational points of certain elliptic curve, called "Legendre curve", and the properties and value distribution of such number are also presented.
基金supported by the National Fundamental Science Research Program 973 of China under Grant No. 2004 CB3180000the State Key Lab. (Information Security) of China
文摘A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic numbers.Then,the authors determine explicitly thecomplexity of such normal bases and their dual bases in several cases where the related cyclotomicnumbers have been calculated.Particularly,the authors find several series of such normal bases withlow complexity.
