Two types of the MacWilliams identities of the Fp+uFp+...+uk-1Fp-linear codes

Error-correcting coding theory is an important theoretieal basis of information security. And the MacWilliams identity of the code is an important branch of error-correcting coding theory. In recent years, the research interest of many scholars engaged in coding theory have been transferred to the finite ring. Researches on MacWilliams identities over finite rings have not only important theory meanings but also important practical value. Many achievements about the weight distribution of the code over the ring have been made. Let R = Fp+uFp+...+uk-1Fp. In this study, the MacWilliams identities of the R-linear codes are discussed. Firstly, the complete weight enumerator and the symmetrized weight enumerator of R-linear codes are defined. Secondly, the complete weight MacWilliams identity and the symmetrized weight MacWilliams identity are given by using a special variable t. Finally, an example are given to show the use of two types of MacWilliams identities. This study improves the error-correcting coding theory of the ring R and promotes its actual application. © 2013 Asian Network for Scientific Information.