最佳跳频序列族的设计与分析

本文提出了基于ｐ元广义ＧＭＷ序列和ｐ元Ｋａｓａｍｉ序列构造跳频序列族的方法,证明了基于广义ＧＭＷ序列所构造的跳频序列族具有最佳Ｈａｍｍｉｎｇ相关特性,而基于Ｋａｓａｍｉ序列所构造的跳频序列族不具有最佳Ｈａｍｍｉｎｇ相关特性。     

基于三元伪随机序列集的多声源房间脉冲响应测量方法*

在多输入多输出系统中,诸多情况下需并行测量任意输入输出之间的脉冲响应。虽然利用以Kasami序列集为代表的二元伪随机序列集良好的相关特性可以实现多声源并行测量,但是囿于其编解码信号相同且为二元信号的特点,使得其相关特性仍存在较大的可优化空间。该文提供了一种基于三元伪随机序列集的多声源房间脉冲响应测量方法,具有更好的相关特性,提高了测量准确度。仿真和实验验证了该测量方法的可行性和准确性。在封闭空间几何模型构建等领域中,可使用该方法提高测量效率并降低由于各通道不同步导致的误差。     

Direct constructions of additive codes

A code is q^m‐ary q‐linear if its alphabet forms an m‐dimensional vector space over ??_q and the code is linear over ??_q. These additive codes form a natural generalization of linear codes. Our main results are direct constructions of certain families of additive codes. These comprise the additive generalization of the Kasami codes, an additive generalization of the Bose‐Bush construction of orthogonal arrays of strength 2 as well as a class of additive codes which are being used for deep space communication. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 207–216, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.20000     

扩展Kasami序列的相关特性

利用有限域上二次型理论讨论了ｐ（ｐ为奇素数）元Ｋａｓａｍｉ序列一种扩展形式的相关特性，求出了扩展Ｋａｓａｍｉ序列的相关函数值，证明在一定条件下，扩展Ｋａｓａｍｉ序列最大自相关旁瓣值和最大互相关模值可以接近Ｗｅｌｃｈ下限．     

浅水多波束高帧率测深技术研究

针对常规多波束测量中由于远距离目标信号未到达接收基阵而不能再次发射探测信号,导致测深帧率下降的问题,提出了基于Kasami编码的浅水多波束高帧率测深方法。首先讨论了频分复用高帧率测深方法、基于Kasami编码的并行高帧率测深方法和串行高帧率测深方法的原理,然后通过仿真对比了三种方法的条带间干扰和测深精度的性能,最后分析表明基于Kasami编码的串行高帧率测深方法具有较低的条带间干扰能力和较高的测深精度。最后采用国产首套浅水宽覆盖多波束测深系统进行了水池实验验证,结果表明该方法在保证测量精度的情况下,可有效的提高测量帧率。     

Plateaudness of Kasami APN functions

It is shown that the Kasami function defined on ${\mathbb{F}}_{2^n}$ with n even is plateaued. This generalizes a result [3, Theorem 11], where the restriction $(n,3)=1$ is assumed. The result is used to establish the CCZ-inequivalence of the Kasami function defined on ${\mathbb{F}}_{2^n}$ with n even to the other known monomial APN functions [4].     

The chromatic number and rank of the complements of the Kasami graphs

We determine the rank and chromatic number of the complements of all Kasami graphs, some of which form an infinite family of counterexamples to the now disproven rank-coloring conjecture.     

Two results on maximum nonlinear functions

Maximum nonlinear functions are widely used in cryptography because the coordinate functions F _β (x) := tr(β F(x)), , have large distance to linear functions. Moreover, maximum nonlinear functions have good differential properties, i.e. the equations F(x + a) − F(x) = b, , have 0 or 2 solutions. Two classes of maximum nonlinear functions are the Gold power functions , gcd(k, m) = 1, and the Kasami power functions , gcd(k, m) = 1. The main results in this paper are: (1) We characterize the Gold power functions in terms of the distance of their coordinate functions to characteristic functions of subspaces of codimension 2 in . (2) We determine the differential properties of the Kasami power functions if gcd(k,m) ≠ 1.