The central trinomial coefficient T_(n)denotes the coefficient of x^(n)in the expansion of(1+x+x^(2))^(n).We prove a congruence related to the sums of the central trinomial coefficient and the central binomial coeffic...The central trinomial coefficient T_(n)denotes the coefficient of x^(n)in the expansion of(1+x+x^(2))^(n).We prove a congruence related to the sums of the central trinomial coefficient and the central binomial coefficient,which was conjectured by Z.-W.Sun.展开更多
正规基在有限域的许多应用领域中有广泛应用:编码理论、密码学、信号传送等.Z.X.Wan等(Finite Fields and Their Applications,2007,13(4):411-417.)给出了Fqn在Fq上的Ⅰ型最优正规基的对偶基的复杂度为:3n-3(q为偶数)或3n-2(q为奇数)....正规基在有限域的许多应用领域中有广泛应用:编码理论、密码学、信号传送等.Z.X.Wan等(Finite Fields and Their Applications,2007,13(4):411-417.)给出了Fqn在Fq上的Ⅰ型最优正规基的对偶基的复杂度为:3n-3(q为偶数)或3n-2(q为奇数).这是一类类似于k-型高斯正规基的低复杂度正规基.最近,廖群英等(四川大学学报:自然科学版,2010,47(6):1221-1224.)给出了2-型高斯正规基的对偶基及其复杂度.在此基础上,给出了一般的k-型高斯正规基N的对偶基以及当n≥k≥1时,N的复杂度的一个上界.进而证明了当k=3时,此上界可达到,并由此给出了所有(弱)自对偶的k-型高斯正规基.展开更多
基金National Natural Science Foundation of China(11971222,12071208)Jiangsu Qinglan ProjectProject of Guangzhou Huashang College(2022HSDS27)。
文摘The central trinomial coefficient T_(n)denotes the coefficient of x^(n)in the expansion of(1+x+x^(2))^(n).We prove a congruence related to the sums of the central trinomial coefficient and the central binomial coefficient,which was conjectured by Z.-W.Sun.
文摘正规基在有限域的许多应用领域中有广泛应用:编码理论、密码学、信号传送等.Z.X.Wan等(Finite Fields and Their Applications,2007,13(4):411-417.)给出了Fqn在Fq上的Ⅰ型最优正规基的对偶基的复杂度为:3n-3(q为偶数)或3n-2(q为奇数).这是一类类似于k-型高斯正规基的低复杂度正规基.最近,廖群英等(四川大学学报:自然科学版,2010,47(6):1221-1224.)给出了2-型高斯正规基的对偶基及其复杂度.在此基础上,给出了一般的k-型高斯正规基N的对偶基以及当n≥k≥1时,N的复杂度的一个上界.进而证明了当k=3时,此上界可达到,并由此给出了所有(弱)自对偶的k-型高斯正规基.
