关于哥德巴赫猜想度法证明的研究探讨

"每个偶数既都是两个奇素数之和又都是俩奇数之和",度法可以通解两和。奇素数既是奇数又是素数。随着奇数的增大,尽管素奇比越来越小而两者度法2的相似度非但不小反而增大直到相似一样。     

每个大于1的奇数都是三个奇素数之和

每个整数P(1,i)一之中一之又一不但能把"每个偶数都是两个奇素数之和"直接表示出来而且还能把"每个大于1的奇数都是三个奇素数之和"直接表示出来。两个命题都是一个规律。     

周期长度为奇素数的伪随机序列的功率谱分析

本文分析了奇素数有限域中平方剩余的某些性质，介绍了长度为奇素数的伪随机序列的构造和产生方法，简明地证明了这些序列的自相关函数，最后推导出了奇素数ｑ≡１（ｍｏｄ４）序列的功率谱表达式。     

周期长度为奇素数N=4x＋1的伪随机序列

分析了奇素数有限域中元素的某些性质，介绍了周期长度为奇素数N=4x＋1的伪随机序列的构造，指出了这种伪随机序列的优良特性，并与其它伪随机序列作了比较。     

广义bent序列的构造

首先给出了一些二次bent函数在F2^n上的迹函数的表示，考虑了有限F2^n研为偶数）上Gold函数tr1^n（x^2i＋1），1≤i≤n-1，在丘上的线性组合，添加一项tr1^n/2（x^2n/2＋1）后所得函数构成bent函数的充分必要条件，类似于Khoo等人给出的结果，可以通过计算多项式的最大公因式来验证这个条件，并把这个结论推广到Fp^n（n为偶数，p为奇素数）的情形。最后利用得到的结果以及Dobbertin等人构造的Niho型bent函数构造了新的广义bent序列。     

确定周期序列线性复杂度的快速算法

本文介绍了确定周期序列的线性复杂度的两个快速算法。一个适应于GF（q)上周期为p^n的序列,另一个适应于GF（p^m)上周期为p^n的序列,这里p是奇素数,q是素数并且是模p^2的本原根。     

一类超椭圆曲线上的快速除子标量乘

 除子标量乘是超椭圆曲线密码体制中的关键运算.基于单除子标量乘的思想,将Duursma与Sakurai给出的关于奇素数域上一类特殊超椭圆曲线上的一个除子标量乘算法推广到奇素数域扩域上更一般的此类超椭圆曲线上,得到了两个效率更高的公式化的除子标量乘新算法.这两算法所需的运算量比二元法降低12%以上.     

素数长理想平衡四元几乎失配互补对构造

当一对失配序列的所有异相自相关函数和均为同一非0整数时，称该对失配序列为几乎失配互补对。该文提出平衡4元几乎失配互补对的新类型序列，通过Gray映射证明得到了平衡的素数长4元几乎失配互补对的理论界，基于4阶分圆类，提出满足理论界的周期为素数长的理想平衡4元几乎失配互补对的构造方法。通过该文研究扩大了4元互补对的存在范围，弥补了目前已有4元互补对大多只存在偶数长度的缺陷。     

复合测距码及其子码 第二部份 用以组成复合测距码的子码

这里共讨论了四种可用以组成复合测距码的子码,即最长周期序列,周期为P=2×奇数 1的素数的最优二进序列,周期为P=2×偶数 1的素数的准最优二进序列以及周期为13的另一类准最优二进序列。这些序列不仅可用以组成复合测距码,而且在其它方面也很有用处。例如最长周期序列可作为许多通信和控制系统的测试信号,也可用作密码。其余三种序列是导出许多有良好自相关特性的脉冲压缩码的桥樑。     

一类新的周期为2pq的二元广义分圆序列的线性复杂度

该文提出一类新的周期为2pq, p和q为不同奇素数的广义分圆序列,并给出了该序列线性复杂度的计算公式。在已知序列支撑集的情况下,利用该公式可以得到该序列线性复杂度的精确值。     

On the binary quadratic residue system with noncoprime moduli

The residue number system (RNS) appropriate for implementing fast digital signal processors since it can support parallel, carry-free, high-speed arithmetic. A development in residue arithmetic is the quadratic residue number system (QRNS), which can perform complex multiplications with only two integer multiplications instead of four. An RNS/QRNS is defined by a set of relatively prime integers, called the moduli set, where the choice of this set is one of the most important design considerations for RNS/QRNS systems. In order to maintain simple QRNS arithmetic, moduli sets with numbers of forms 2ⁿ+1 (n is even) have been considered. An efficient such set is the three-moduli set (2^2k-2+1.2^2k+1.2^2k+2+1) for odd k. However, if large dynamic ranges are desirable, QRNS systems with more than three relatively prime moduli must be considered. It is shown that if a QRNS set consists of more than four relatively prime moduli of forms 2ⁿ+1, the moduli selection process becomes inflexible and the arithmetic gets very unbalanced. The above problem can be solved if nonrelatively prime moduli are used. New multimoduli QRNS systems are presented that are based on nonrelatively prime moduli of forms 2ⁿ +1 (n even). The new systems allow flexible moduli selection process, very balanced arithmetic, and are appropriate for large dynamic ranges. For a given dynamic range, these new systems exhibit better speed performance than that of the three-moduli QRNS system     

17 does not divide the order of the group of a (72,36,16) doubly even code (Corresp.)

It is an interesting open question whether an extremal (72, 36, 16) doubly even code C exists. In [3] the odd prime numbers which can divide the order of the group of C were determined. The largest of these, 23, was eliminated by finding weight 12 vectors in 384 codes [8]. The next largest prime remaining is 17. It is shown that 17 is also not possible by reducing the problem to the consideration of16.17^{3}codes and then finding a weight 12 vector, by computer, in each of these codes.     

The vulnerability of geometric sequences based on fields of odd characteristic

A new method of cryptologic attack on binary sequences is given, using their linear complexities relative to odd prime numbers. We show that, relative to a particular prime number p, the linear complexity of a binary geometric sequence is low. It is also shown that the prime p can be determined with high probability by a randomized algorithm if a number of bits much smaller than the linear complexity is known. This determination is made by exploiting the imbalance in the number of zeros and ones in the sequences in question, and uses a new statistical measure, the partial imbalance.This project was sponsored by the National Security Agency under Grant No. MDA904-91-H-0012. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation hereon.     

Ordering of Walsh Functions

The construction of Walsh functions is derived by means of the concepts of "symmetric copy" and "shift copy." Recursive relations based on the Kronecker product of matrices are also deduced from these concepts. There is a fourth useful ordering of the Walsh functions, called here X-ordering, in addition to the three known orderings usually referred to as Walsh-, Paley-, and Hadamardordering. An X-ordering function has the following features: lower order numbers of X-ordering correspond to even functions; higher order numbers of X-ordering correspond to odd functions; even order numbers of X-ordering correspond to lower sequencies; odd number of X-ordering correspond to higher sequencies. Finally, relations between the four orderings are given.     

Transitional MURROMAF-MURROER filters with additional members

Recently, a method [4] has been described for the design of transitional MURROMAF-MURROER filters whose members exhibit odd numbers of passband ripple peaks. An additional technique is proposed here to find also those with even numbers of the ripple peaks. Hence, transitional MURROMAF-MURROER filters with complete transitional members.     

Binary self-dual codes with automorphisms of composite order

In this paper, we present some results concerning a decomposition of binary self-dual codes having an automorphism of an order which is the product of two odd prime numbers. These results are applied to construct self-dual [72,36,12] codes with an automorphism of order 15. Furthermore, it is proved that the automorphism group of a putative binary extremal self-dual [72,36,16] code contains at most 28 nontrivial types of automorphisms of odd order. A complete list of these possible types of automorphisms is presented.     

领头项奇偶相干态

奇相干态只呈现反群聚而绝无压缩，偶相干态正好与之相反，只有压缩而无反群聚性。为了从内部窥视下一奇偶相干态的这种独特的非经典性是怎样产生的，我们引入一类新的量子光场态－领头项奇偶相干态。通过对这些量子态的研究，清楚地揭示出随着领头项奇偶相干态中项数的增多，它们的性质是怎样趋于奇偶相干态的。     

Decoding the Johnson code by 2-output comparator circuits

The problem of decoding the n-bit Johnson code to decimal numbers is discussed. For an odd number n, a systematic procedure is possible utilising n 2-input 2-output comparator circuits. A theorem is stated and proved for the nonexistence of such a procedure when n is even.     

一种卫星导航抗干扰天线数字信号正交分解方法

提出了一种基于 FIR 滤波器的卫星导航抗干扰天线数字信号正交分解方法。首先, 根据卫星导航信号在抗干扰天线中的中频中心频率及带宽信息确定带通滤波器的通带、阻带响应以及滤波器阶数等参数。接下来,采用 Parks-McClellan 算法分别设计滤波系数偶对称和奇对称的带通滤波器。最后,将抗干扰天线中 AD 采样后的中频数字实信号分别通过以上偶对称和奇对称的带通滤波器即可得到 I、Q 两路信号。本文所提方法具有计算量小、精度高且易于工程实现的特点。通过对实测数据分析验证了本文所提方法的有效性。     

A 3-dB directional coupler for microwave integrated circuits

A procedure for designing quarter-wavelength 3-dB directional couplers is described which utilizes a perturbation technique to reduce the number of experimental models needed during the development. Limitations caused by unequal odd and even mode phase velocities and junction parasitics are discussed. The use of thin-film conductors on quartz and glazed ceramic gives a coupling accuracy better than 3.0 ± 0.1 dB and an isolation greater than 32 dB with worst-case tolerances.