一种求循环码单位元的新方法

循环码单位元和生成函数可生成理想的不同生成元。单位元以其独特性的性质在编译码理论分析和实用通信系统纠检错设计中发挥了很大的作用。由于它不像生成函数那样直观，对它的研究还很不充分，本文提出一种利用有限域ＧＦ（ｑ＾ｍ）上离散傅里叶变换（ＤＦＴ）来求循环码单位元的新方法，着重分析了有限域上时域多项环的理想和它ＤＦＴ之间的同构。应用这种方法可以求得任意ＧＦ（２）上循环码的单位元。与以往的时域分析法相比具有

A New Method for Finding the Identity Element of Cyclic Codes

identity element and generator polynomial are two different generators of the ideal.The identity element plays an important role in practical communication system as well as in theoretical analysis of encoding and decoding for its unique characteristics. Research based on its properties is far from sufficient because identity element is not as intuitive as generator polynomial of cyclic code. In this paper a new method is presented to find the identity element of cyclic code using discrete fourier transform (DFT) over GF(qm). The paper puts emphasis On ideal isomorphism between polynomial ring of time domain and its DFT over GF(qm). The identity element of arbitrary cyclic code over GF(2) can be found out by use of this method.The advantage of this method is distinct in its notion,and simple in its means as compared with the other analyses of time domain. Finally,the illustrative examples of this method is given in detail.