Circulant Matrix Theory On Skew Field And Application In Coding Theory

Circle matrix is a new subject . The concept of circle matrix is advanced by Muir.T. who is a scholar of American .Before the year of 1950,the research about circle matrix didn't be recognition by most of the scholars ,those years, especially after the year of 1950,with the development of modern technology,people found that circle matrix had many application in fact .such as Coding ;Stat ;Geometry ;Oil reconnaissance ;Configuration analyse ;Treating numeral image and so on .There are more and more application in those aspect.In this paper ,we discuss the theory of circle matrix on skew field and its application in Coding theory, the conclusion we got in the last have some theory sense and application value. This study mostly be discuss to three aspects: First , defined circle matrix on skew field and discuss the theory of its property; Second , discuss the way to get the contradiction of circle matrix on skew field; Third ,study the application of circle matrix on skew field on the theory of coding .The mostly contents are as following , Introduce the background of the theory of circle matrix and the application of circle matrix on the theory of coding in brief; Look back the conclution and basic notion which will be used in this paper ; From comparing the different operation between field and skew field, definded the theory of circle matrix on skew field and the application of circle matrix on skew field on the theory of coding; By comparing the different operation between field and skew field, discuss the way to get the contradiction of circle matrix on skew field; Defined the linearity code and circle code on skew field ,discuss the application of the theory of circle matrix on skew field in Coding theory; From analyzing the characters of circle code , get a simple method of the way to work-out the creation polynomial of circular code with primary transform of matrix.