With Regard To A Number Of Writing Method Of Cyclic Codes

1957, Prange first introduced the concept of cyclic codes, and code polynomial representation, since then, the theory of block codes, especially in the theory of cyclic codes has been the rapid development of. The significant advantage of cyclic codes is that it's coding and can be calculated with a simple shift register with feedback connections to achieve the other, because cyclic codes have a good algebraic properties, one can use "algebra" is a powerful mathematical tools to conduct in-depth study of cyclic codes, and find a variety of simple and efficient decoding method. Fu fang wei in the literature [1] studied the distribution of cyclic codes of the cycle of new formula, Wang xin mei,Xiao guo zhen in the literature [2] of the error-correcting codes of principles and methods described in detail; Shan yi xian in the literature [3] described in detail in the realization of cyclic codes forward error correction method and the first of applications, studied the realization method and application of cyclic code theory; Deng you-e in the literature [4] introduced a cyclic code error-correcting coding and decoding of the application in the analysis of the mathematical principle of cyclic codes are discussed with strong inspection, the cycle of error-correcting capability code implementation method; Zhou huan-yin in the literature [5] of the traditional writing method improved cyclic code and in accordance with the characteristics of cyclic codes, cyclic codes summed up writing a simple and convenient without error-prone method.The author's key findings:1. Through the existing loop coding method, analysis, summary, proposed a new binary cyclic codes of writing a number of ways;2. Summarizes the cyclic code from high to low "0" and "1" changes of the distribution, combined with the cyclic changes of the symmetry code given number of cyclic binary code written in another way;3. After extensive research, combined with two adjacent minterm Karnaugh map logical neighbors, but also clear and intuitive features. A variable k (k > 6), the Karnaugh map method of making and apply it to writing a number of cyclic binary code.