Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2013.5744.5748p+uF_{p}+...+u^{k-1}F_{p}-Linear
Codes]]>XuXiaofangShujie Yun1220131324Error-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 = F_{p}+uF_{p}+...+u^{k-1}F_{p}.
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.]]>Hammons, A.R., P.V. Kumar, A.R. Calderbank, N.J.A. Sloane and P. Sole,19944-linearity of Kerdock, Preparata, Goethals and related codes.]]>Shiromoto, K.,1996Wan, Z.X.,1997Cui, J. and J.Y. Pei,2004Shi, M.J., S.X. Zhu and P. Li,20082+vF_{2}.]]>Liang, H. and Y.S. Tang,2010F_{2} + uF_{2} + u^{2}F_{2}.]]>Li, Y. and L.S. Chen,2010F_{p} + uF_{p}.]]>Yildiz, B. and S. Karadeniz,20102+uF_{2}+vF_{2}+uvF_{2}.]]>Xu, X.F. and Q.L. Mao,2013F_{p} + uF_{p} + u^{2}F_{p}.]]>