设p为奇质数,q=p^(n)(n∈Z^(+)),f(x)∈F_(q)[x].Wan(Journal of Systems Science and Complexity,2021,34(4):498-510.)研究了指数和S_(q)(f(x))的代数次数及周期性.特别地,陈超等(四川大学学报(自然科学版),2020,57(6):1029-1032.)证...设p为奇质数,q=p^(n)(n∈Z^(+)),f(x)∈F_(q)[x].Wan(Journal of Systems Science and Complexity,2021,34(4):498-510.)研究了指数和S_(q)(f(x))的代数次数及周期性.特别地,陈超等(四川大学学报(自然科学版),2020,57(6):1029-1032.)证明了p≡-1(mod d)且q=p^(2)时,S_(q)(x^(d))=-p或(d-1)p.基于上述结果,讨论p≡-1(mod d)且q=p^(2r)(r∈Z^(+))时S_(q)(x^(d))的具体取值,进而利用初等的方法和技巧,得到deg S_(q)(x^(d))=1时,S_(q)(x^(d))的全部可能取值.展开更多
为将Lehmer同余式的模从素数的平方推广到任意整数的平方,Cai等(CAI T X,FU X D,ZHOU X.Acta Aritmetica,2007,130(3):203-214.)定义了广义欧拉函数φ_(e)(n),给出了e=3,4,6时广义欧拉函数φ_(e)(n)的计算公式.最近Zhu等(ZHU C Z,LIAO Q...为将Lehmer同余式的模从素数的平方推广到任意整数的平方,Cai等(CAI T X,FU X D,ZHOU X.Acta Aritmetica,2007,130(3):203-214.)定义了广义欧拉函数φ_(e)(n),给出了e=3,4,6时广义欧拉函数φ_(e)(n)的计算公式.最近Zhu等(ZHU C Z,LIAO Q Y.arXiv:2105.10870v1,2021.)确定了e=5时φ_(e)(n)的准确计算公式.利用初等的方法和技巧,研究方程φ_(5)(n)=2^(ω(n))的可解性,确定其全部正整数解.展开更多
Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an o...Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p,the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.展开更多
文摘设p为奇质数,q=p^(n)(n∈Z^(+)),f(x)∈F_(q)[x].Wan(Journal of Systems Science and Complexity,2021,34(4):498-510.)研究了指数和S_(q)(f(x))的代数次数及周期性.特别地,陈超等(四川大学学报(自然科学版),2020,57(6):1029-1032.)证明了p≡-1(mod d)且q=p^(2)时,S_(q)(x^(d))=-p或(d-1)p.基于上述结果,讨论p≡-1(mod d)且q=p^(2r)(r∈Z^(+))时S_(q)(x^(d))的具体取值,进而利用初等的方法和技巧,得到deg S_(q)(x^(d))=1时,S_(q)(x^(d))的全部可能取值.
文摘为将Lehmer同余式的模从素数的平方推广到任意整数的平方,Cai等(CAI T X,FU X D,ZHOU X.Acta Aritmetica,2007,130(3):203-214.)定义了广义欧拉函数φ_(e)(n),给出了e=3,4,6时广义欧拉函数φ_(e)(n)的计算公式.最近Zhu等(ZHU C Z,LIAO Q Y.arXiv:2105.10870v1,2021.)确定了e=5时φ_(e)(n)的准确计算公式.利用初等的方法和技巧,研究方程φ_(5)(n)=2^(ω(n))的可解性,确定其全部正整数解.
基金supported by the National Natural Science Foundation of China under Grant No.11401408Project of Science and Technology Department of Sichuan Province under Grant No.2016JY0134the National Key R and Program of China under Grant No.2016QY04W080
文摘Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p,the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.
