Simple Convex Polytope And Linear Code

The research of Convex polytope is an important branch of geometry.The modern theory of convex polytope begun in the sixties of the 20 th century,which aroused the mathematicians interest in the study of the convex polytope, especially the research of problems of convex polytope. In addition, in the field of natural science, coding theory is also a key research topic. However, in the area of mathematics, scholars take more interested in staying the linear code(especially self-dual code). scholars study the deeper of the classification of binary self-dual codes.In this paper, the main mission continues the research works of Dr. Chen and other scholars. To further explore the structure of the linear code which combinational convex polytopes generate, especially,the discussion of the structure of the binary self-dual code,which generated by combinational convex polytopes. Meanwhile,the paper also discussed that several binary self-dual codes can be realized by convex polytope, and the minimum distance of self-dual code generated convex polytopes.