Tao Feng

Zhejiang University

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i-10 index

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Qing Xiang

Southern University of Science and Technology

Koji Momihara

Kumamoto University

Gennian Ge

Capital Normal University

Weicong Li

University of Technology Malaysia

Shuxing Li

University of Delaware

Tao Zhang

Guangzhou University

Ran Tao

State Key Laboratory of Cryptology

Sihuang Hu

Shandong University

Yu Qing Chen

Wright State University

San Ling

Nanyang Technological University

Cooperative Institutions

Zhejiang University

Hudson Institute

John Wiley & Sons (United States)

University of Waterloo

Chinese Academy of Sciences

Nanyang Technological University

University of Delaware

Peking University

University of Science and Technology of China

National University of Singapore

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Commenting on Restriction of Abstract Administrative Conducts

Journal of Luoyang Institute of Science and Technology (2012)

Tao Feng

Although a larger scale of performing abstract administrative actions can give rise to many new problems,the existence of the actions has its historical inevitability and rationality.Only by the way of perfecting the system,can the abstract administrative actions be ensured and carried out impartially.From the aspects of formulating procedures on the basis of abstract administrative actions,judicial review system and legal liability of abstract administrative actions,this paper attempts to comment on the supervision and restriction on the further perfection of the surveillance of abstract administrative actions.

Perfection

Source

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Three-valued Gauss periods, circulant weighing matrices and association schemes

arXiv (Cornell University) (2014)

Tao Feng Koji Momihara Qing Xiang

Gauss periods taking exactly two values are closely related to two-weight irreducible cyclic codes and strongly regular Cayley graphs. They have been extensively studied in the work of Schmidt and White and others. In this paper, we consider the question of when Gauss periods take exactly three rational values. We obtain numerical necessary conditions for Gauss periods to take exactly three rational values. We show that in certain cases, the necessary conditions obtained are also sufficient. We give numerous examples where the Gauss periods take exactly three vlaues. Furthermore, we discuss connections between three-valued Gauss periods and combinatorial structures such as circulant weighing matrices and 3-class association schemes.

Gauss sum

10.48550/arxiv.1409.8350

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Paley type group schemes from cyclotomic classes and Arasu-Dillon-Player difference sets

arXiv (Cornell University) (2012)

Yu Qing Chen Tao Feng

In this paper, we present constructions of abelian Paley type group schemes by using multiplicative characters of finite fields and Arasu-Dillon-Player difference sets. The constructions produce many new Paley type group schemes that were previous unknown in our classification of Paley type group schemes in finite fields of small orders.

10.48550/arxiv.1210.2801

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Some New Results on the Cross Correlation of $m$-sequences

arXiv (Cornell University) (2013)

Tao Zhang Shuxing Li Tao Feng Gennian Ge

The determination of the cross correlation between an $m$-sequence and its decimated sequence has been a long-standing research problem. Considering a ternary $m$-sequence of period $3^{3r}-1$, we determine the cross correlation distribution for decimations $d=3^{r}+2$ and $d=3^{2r}+2$, where $\gcd(r,3)=1$. Meanwhile, for a binary $m$-sequence of period $2^{2lm}-1$, we make an initial investigation for the decimation $d=\frac{2^{2lm}-1}{2^{m}+1}+2^{s}$, where $l \ge 2$ is even and $0 \le s \le 2m-1$. It is shown that the cross correlation takes at least four values. Furthermore, we confirm the validity of two famous conjectures due to Sarwate et al. and Helleseth in this case.

Sequence (biology)

Decimation

Pseudorandom binary sequence

Cross-correlation

10.48550/arxiv.1309.7734

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Algebraic degrees of quasi-abelian semi-Cayley digraphs

arXiv (Cornell University) (2023)

Shixin Wang Majid Arezoomand Tao Feng

For a digraph $\Gamma$, if $F$ is the smallest field that contains all roots of the characteristic polynomial of the adjacency matrix of $\Gamma$, then $F$ is called the splitting field of $\Gamma$. The extension degree of $F$ over the field of rational numbers $\mathbb{Q}$ is said to be the algebraic degree of $\Gamma$. A digraph is a semi-Cayley digraph over a group $G$ if it admits $G$ as a semiregular automorphism group with two orbits of equal size. A semi-Cayley digraph $\mathrm{SC}(G,T_{11},T_{22},T_{12},T_{21})$ is called quasi-abelian if each of $T_{11},T_{22},T_{12}$ and $T_{21}$ is a union of some conjugacy classes of $G$. This paper determines the splitting field and the algebraic degree of a quasi-abelian semi-Cayley digraph over any finite group in terms of irreducible characters of groups. This work generalizes the previous works on algebraic degrees of Cayley graphs over abelian groups and any group having a subgroup of index 2, and semi-Cayley digraphs over abelian groups.

Digraph

Cayley graph

Degree (music)

Cayley's theorem

10.48550/arxiv.2308.03066

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The shift bound for abelian codes and generalizations of the Donoho-Stark uncertainty principle

arXiv (Cornell University) (2018)

Tao Feng Henk D. L. Hollmann Qing Xiang

Let $G$ be a finite abelian group. If $f: G\rightarrow \bC$ is a nonzero function with Fourier transform $\hf$, the Donoho-Stark uncertainty principle states that $|\supp(f)||\supp(\hf)|\geq |G|$. The purpose of this paper is twofold. First, we present the shift bound for abelian codes with a streamlined proof. Second, we use the shifting technique to prove a generalization and a sharpening of the Donoho-Stark uncertainty principle. In particular, the sharpened uncertainty principle states, with notation above, that $|\supp(f)||\supp(\hf)|\geq |G|+|\supp(f)|-|H(\supp(f))|$, where $H(\supp(f))$ is the stabilizer of $\supp(f)$ in $G$.

Sharpening

10.48550/arxiv.1804.00367

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Integrated interferometer for measuring three-dimensional vibrations based on spherical cooperative target

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE (2011)

Xuejie Zhang Dean Liu Tao Feng Fang Liu Jie Miao

This paper proposes a new method for measuring three-dimensional vibrations. By a spherical cooperative target, the system realizes interference from a spherical wave and a plane wave. It solves the problem of complex changes in interference fringes when two spherical waves are used to measure three-dimensional vibration. And the vibration calculation is very simple. Meanwhile, the interferometer integrates two interference arms into a beamsplitter by coating design and can monitor the stability of the system itself. Theoretical analysis and experiment are performed. The experiment results indicate that the method can monitor three-dimensional vibrations accurately.

Beam splitter

10.1117/12.914388

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Outline of the 12th Five Year Development Plan for the Chinese Grain Industry

Cereal Foods World (2013)

Tao Feng

An outline for the 12th Five Year Development Plan for the Grain Industry of China has been drawn up. The plan will be key in developing the grain products industry in China by providing a structure for an improved oversight system, optimized grain reserve regulation, increased grain storage capacity, improved grain and oil standards and inspection systems, and enhanced scientific research and development. Logistics systems for transporting grain from north to south, bulk storage and transportation, and supply chains must be strengthened. The gross value of the grain and oil processing industries should be kept above 12% of the gross national product annually. The plan seeks to improve production operation efficiency, promote the construction of a legal system, and administrate the grain industry through a system of laws.

Development plan

Five year plan

10.1094/cfw-58-3-0160

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Hadamard difference sets related to Lander's conjecture

Journal of Algebra (2014)

Tao Feng Ka Hin Leung Bernhard Schmidt K. Smith

If a Hadamard difference set exists in H×K, where H is an abelian 2-group and K is a cyclic 3-group, then |H|>4|K|. Furthermore, Lander's conjecture holds for all Hadamard difference sets of order at most 529.

10.1016/j.jalgebra.2013.11.027

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On codes in the projective linear group $PGL(2,q)$

arXiv (Cornell University) (2020)

Tao Feng Weicong Li Jingkun Zhou

In this paper, we resolve a conjecture of Green and Liebeck [Disc. Math., 343 (8):117119, 2019] on codes in $PGL(2,q)$. To be specific, we show that: if $D$ is a dihedral subgroup of order $2(q+1)$ in $G=PGL(2,q)$, and $A=\{g\in G: g^{q+1}= 1,\, g^2\ne 1 \}$, then $\lambda G=A\cdot D$, where $\lambda=q$ or $q-1$ according as $q$ is even or odd.

Dihedral group

10.48550/arxiv.2009.01025

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