**会议报告题目和摘要**

**主办：**数学与统计学学院

**时间：**2017年10月14日～15日

**会议地点：**数统学院201报告厅

**报告人：**唐小虎

**所在单位：**西南交通大学

**报告题目：**面向视频分发的缓存编码研究

**报告摘要：**近年来，移动互联网得到了飞速发展，其中视频业务增长巨大．编码缓存技术是视频分发的有效解决手段之一，本报告中我们提出存储发送阵列（PDA）的概念来刻画一类编码缓存方案，不仅可以解释已知的构造，而且能得到新的PDA，相比于已知构造，可以极大地减少视频文件分割的数目，从而降低系统实现复杂度．

**报告人：**屈龙江

**所在单位：**国防科技大学

**报告题目：**Constructing infinite families of low differential uniformity (n,m)-functions with m>n/2

**报告摘要：**Little theoretical work has been done on (n,m)-functions when n/2<m<n, even though these functions can be used in Feistel ciphers, and actually play an important role in several block ciphers. Nyberg has shown that the differential uniformity of such functions is bounded below by 2^{n-m}+2 if n is odd or if m> n/2. In this paper, we first characterize the differential uniformity of those (n,m)-functions of the form F(x,z)=\phi(z)I(x), where I(x) is the (m,m)-Inverse function and \phi(z) is an (n-m,m)-function. Using this characterization, we construct an infinite family of differentially \Delta-uniform (2m-1,m)-functions with m\geq 3 achieving Nyberg's bound with equality, which also have high nonlinearity and not too low algebraic degree. Moreover, it is a balanced vectorial semi-bent function. Then we present a method to construct infinite families of (m+k,m)-functions with low differential uniformity and construct an infinite family of (2m-2,m)-functions with \Delta\leq2^{m-1}-2^{m-6} +2 for any m\geq 8.We also discuss an infinite family of differentially 4-uniform (m+1,m)-functions in this form, which leads to many differentially 4-uniform permutations. The constructed functions in this paper may provide more choices for the design of Feistel ciphers.

**报告人：**杜小妮

**所在单位：**西北师范大学

**报告题目：**基于二次型的线性码设计

**报告人：**岳勤

**所在单位：**南京航空航天大学

**报告题目：**Further factorization of x^n-1 over a finite field

**报告摘要：**Let Fq be a finite field with q elements and n a positive integer. Mart\'{\i}nez, Vergara and Oliveira \cite{MVO} explicitly factorized x^{n} - 1 over Fq under the condition of rad(n)|(q-1). In this paper, suppose that rad(n)\nmid (q-1) and rad(n)|(q^w-1), where w is a prime, we explicitly factorize x^{n}-1 into irreducible factors in Fq[x] and count the number of its irreducible factors.

**报告人：**胡红钢

**所在单位：**中国科技大学

**报告题目：**New constructions of bent functions with simple form

**报告摘要：**In this talk, we show two classes of bent functions with very simple trace representation, which have not been reported in the literature previously.

**报告人：**李念

**所在单位：**湖北大学

**报告题目：**A survey on the application of Niho exponents

**报告摘要：**Niho exponent was originally introduced by Niho who investigated the cross-correlation between an m-sequence and its decimation in 1972. Since then, Niho exponents were further studied and had been used in other research topics. In this talk, we will introduce some research problems related to Niho exponents and present some recent developments.

**报告人：**柯品惠

**所在单位：**福建师范大学

**报告题目：**New classes of zero-difference balanced functions and their applications

**报告摘要：**Zero-difference balanced (ZDB) functions, which have many applications in coding theory and sequence design, have received a lot of attention in recent years. In this talk, based on two known classes of ZDB functions, a new class of ZDB functions is presented by using the Chinese Remainder Theorem (CRT). The new ZDB function is defined on the ring (\mathbb{Z}_{2^{e}-1}\times \mathbb{Z}_{n},+), where e is a prime and n=p_{1}^{m_{1}}p_{2}^{m_{2}}\cdots p_{k}^{m_{k}}, p_{i} is odd prime for any 1\leq i\leq k and \mathrm{gcd}(2^{e}-1,n)=1. Our construction gives ZDB functions with parameters not covered in the literature. As applications, we construct optimal constant composition codes, optimal and perfect difference systems of sets and optimal frequency-hopping sequences by using the new obtained ZDB functions.

**报告人：**杨洋

**所在单位：**西南交通大学

**报告题目：**Construction of Golay complementary sequence sets under spectral hole constraint

**报告摘要：**Orthogonal frequency division multiplexing (OFDM) is an effective method for robustness against multipath interference and Doppler shifts, and it is being used in 5G and the next generation of wireless local area networks (WLAN) for bandwidth efficiency. OFDM sequences have been used for random access, channel estimation, and synchronization. Due to that certain sub-carriers are reserved, i.e., DC sub-carriers and sub-carriers at spectrum edges used for guard interval, the constructions of OFDM sequences under spectral hole constraint naturally become a very important topic. In this paper, we will present some new constructions of such kind of Golay pairs and Golay complementary sequences.

**报告人：**闫统江

**所在单位：**中国石油大学（华东）

**报告题目：**ZUC算法中分位序列的伪随机性质研究

**报告摘要：**祖冲之算法集（ZUC算法）是由我国学者自主设计的加密和完整性算法，已经被国际组织3GPP批准为4G无线通信的第三套国际加密和完整性标准算法，也是我国第一个成为国际标准的密码算法，所以分析其密钥流序列的伪随机性质是十分必要的．我们首先给出了分位序列自相关函数值的分布，进而给出了序列的2-adic复杂度．结果表明分位序列的自相关和2-adic复杂度指标满足设计要求．

**报告人：**查正邦

**所在单位：**洛阳师范学院

**报告题目：** New results on permutation polynomials of the form over

**报告摘要：**Permutation polynomials over finite fields have significant applications in coding theory, cryptography, combinatorial designs and many other areas of mathematics and engineering. In this talk, we study the permutation behavior of polynomials with the form over the finite field . By using the Akbary-Ghioca-Wang (AGW) criterion, we present several new classes of permutations over based on some bijections over the set or the subfield .

**报告人：**伍高飞

**所在单位：**西安电子科技大学

**报告题目：**A new method to construct Golay complementaryset by paraunitary matrices and Hadamard matrices

**报告摘要：**Golay complementary sequences have been highly regarded for decades since their desired properties. However, as the increasing of length, the code rate of standard Golay sequences suffers a dramatic decline for the application in OFDM systems. Even though a lot of effort have been made to solve this drawback, the problem that how to construct large classes of sequences with low PMEPR is still unsolved and open now. In this paper, we proposed a new method to construct q-ary Golay complementary set of size T and length T^m by Hadamard matrices of order T, where m is an integer and T is a power of 2. Every item of the sequences constructed by the new method can be represented as the product of specific entries of the involved Hadamard matrices. Some previous work can be regarded as special cases of the construction in this paper. In particular, new quaternary Golay sets of size 4 and algebraic degree 3 never reported in the literature can be obtained by the proposed method.