关键方程的新推广

给出了关键方程的全新的推广,构造了一个齐次关键模方程,并用域F上的两个变元的多项式环Fx,y]的齐次理想刻画该方程的解空间;证明了齐次关键模方程可以用来解决卷积码的盲识别问题,这是一个全新的研究课题,在智能通信、信息截获和密码分析等领域有重要的应用;利用该方法得到的二元多项式齐次理想Gr（o）bner基的快速算法,给出了求解齐次关键模方程的快速算法,也给出了详细的计算实例.大量的实验也证实了该文的各项理论分析结果.

A New Generalization of Key Equation

This paper proposes a new generalization of the Key Equation. The authors construct a Homogenous Key Module Equation which is described by homogenous ideal of Fx,y], where F is a field. The authors show that the Homogenous Key Module Equation can be used to solve the problem of blind recognition of convolutional codes, which is a novel important research topic in adaptive communication, information interception and cryptanalysis. By means of a fast computation of Groebner basis of homogenous polynomial ideal with two variables, the authors find an efficient algorithm to solve the Homogenous Key Module Equation. A detailed computation example is given in this paper. Extensive experimentation confirms each result of theoretic analysis.