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ON THE COMPLEXITY OF THE NORMAL BASES VIA PRIME GAUSS PERIOD OVER FINITE FIELDS

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Journal of Systems Science & Complexity 2009年第3期22卷 395-406页

作者： qunying liao Keqin FENG College of Mathematics and Software Science Sichuan Normal University Chengdu 610066 China Departmentof Mathematical Sciences Tsinghua University Beijing 100084 China. Department of Mathematical Sciences Tsinghua University Beijing 100084 China.

A formula on the complexity of the normal bases generated by prime Gauss period overfinite fields is presented in terms of cyclotomic ***,the authors determine explicitly thecomplexity of such normal bases and their dual bases in several cases where the related cyclotomicnumbers have been ***,the authors find several series of such normal bases withlow complexity.

关键词： Complexity cyclotomic number finite field Gauss period normal basis.

A new construction for involutions over finite fields

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Frontiers of Mathematics in China 2022年第4期17卷 553-565页

作者： Zhaohui ZHANG qunying liao College of Mathematical Science Sichuan Normal UniversityChengdu610066China

In 2020,Niu et al.[***.,2020,12(2):165–185]studied the fixed points of involutions over the finite field with *** paper further discusses the relationship between the fixed points set and the non-fixed points set of two involutions f_(1)(x)and f_(2)(x)over the finite field F_(q),and then obtains a necessary and sufficient condition for that the composite function f_(1)■f_(2)(x)is also an involution over F_(q).In particular,a special class of involutions over some finite fields is determined completely.

关键词： Permutation polynomial involution fixed point non-fixed point

On Constacyclic Codes over Zp1p2…pt

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Chinese Annals of Mathematics,Series B 2019年第4期40卷 555-566页

作者： Derong XIE qunying liao College of Mathematical Science Sichuan Normal University

Let t ≥ 2 be an integer, and let p1, ···, ptbe distinct primes. By using algebraic properties, the present paper gives a sufficient and necessary condition for the existence of non-trivial self-orthogonal cyclic codes over the ring Zp1p2···ptand the corresponding explicit enumerating formula. And it proves that there does not exist any self-dual cyclic code over Zp1p2···pt.

关键词： Ideal Isomorphism Constacyclic code Self-orthogonal code Self-orthogonal cyclic code

Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications

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Journal of Systems Science & Complexity 2019年第3期32卷 947-969页

作者： LIU Haibo liao qunying WANG Xiaofeng 不详 Institute of Mathematics and Software Science Sichuan Normal University College of Mathematics and Statistics Shenzhen University

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.

关键词： Authentication codes complete weight enumerator constant composition codes exponential sums linear codes secret sharing schemes weight distributions

On the Existence for Some Special Primitive Elements in Finite Fields

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Chinese Annals of Mathematics,Series B 2016年第2期37卷 259-266页

作者： qunying liao Jiyou LI Keli PU College of Mathematics and Software Science Sichuan Normal University Department of Mathematics Shanghai Jiao Tong University Department of Mathematics and Finance Economics Aba Teachers College

Let F_q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive elementα∈ F_(q^n) such that α + α^(-1)is also ... 详细信息

关键词： Finite field Primitive element Normal basis

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广义欧拉函数的计算公式

中国科学技术大学学报 2019年第8期49卷 614-619页

作者：廖群英四川师范大学数学科学学院四川成都610068

设n和e均为正整数.利用初等的方法和技巧,给出了广义欧拉函数φe(n)(e=pr,∏ti=1qi)在所有的qi同余于p均模1或者均模-1时的准确计算公式,其中,p,q1,…,qt为不同的素数,t和r为正整数.这推广了前人的结果.

关键词：欧拉函数广义欧拉函数莫比乌斯函数

一类特殊的near-perfect数（英文）

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中国科学技术大学学报 2017年第11期47卷 906-911页

作者：李建廖群英四川师范大学数学与软件科学学院四川成都61066

设正整数α≥2,p_1,p_2为奇质数且p_1 详细信息

设正整数α≥2,p_1,p_2为奇质数且p_1

关键词： perfect数 near-perfect数冗余因子 k弱near-perfect数

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有限域上一些新的置换多项式(英文)

数学进展 2016年第1期45卷 57-60页

作者：廖群英四川师范大学数学与软件科学学院成都四川610066

关于置换多项式的研究已有多年,并被广泛应用于编码、密码和组合设计.本文利用有限域的性质构造了几类新的置换多项式.

关键词：有限域置换多项式迹映射

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两类广义欧拉函数的递归公式

四川师范大学学报（自然科学版） 2020年第6期43卷 739-746页

作者：廖群英四川师范大学数学科学学院四川成都610066

设n和e均为正整数.近年来,为把著名的Lehmer同余方程的模由素数的平方推广至模任意正整数的平方,文献(*** Aritmetica,2002,103(4):313-320.)定义了正整数n的广义欧拉函数φe(n),并完全确定了φe(n)(e=3,4,6)的准确计算公式.利用初等的... 详细信息

设n和e均为正整数.近年来,为把著名的Lehmer同余方程的模由素数的平方推广至模任意正整数的平方,文献(*** Aritmetica,2002,103(4):313-320.)定义了正整数n的广义欧拉函数φe(n),并完全确定了φe(n)(e=3,4,6)的准确计算公式.利用初等的方法和技巧推广上述结果,给出φe(n)(e=p^t或者e=p^rq^t)的递归计算公式,进而,对一些特殊情形还确定了其准确计算公式.

关键词：欧拉函数广义欧拉函数莫比乌斯函数