Formally Self-dual Codes Over F_q+uF_q

With the rapid development of science and technology, the digital computers and digital communications put forward many mathematical problems with important application background, including the mathematical theory of error-correcting codes which established by the reliability requirements of digital communications. The reliability of communication proposed correction requirements, and established a clear mathematical concepts and problems, and then mathematicians use a combination of science, elementary number theory, algebraic geometry and other mathematical tools to construct better and better error-correcting codes to meet the needs of the project.Formally self-dual codes are an important class of code, it has good algebraic structure and occupies an important position in coding theory. The past two decades, codes over finite rings have been studied by many authors. many scholars have studied cyclic code and self-dual codes over Fq+uFq. This article is based on these to construct formally self-dual codes over Fq+uFq.In this paper, firstly, we define Gray mapping and study properties of Gray mapping images. Then we give four different methods to construct formally self-dual codes on Fq+uFq.