The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F2 ＋ u F2 ＋ v F2 are defined and Gray map from R^nto F2^3n is constructed. By proving the fact that the Gray images o...The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F2 ＋ u F2 ＋ v F2 are defined and Gray map from R^nto F2^3n is constructed. By proving the fact that the Gray images of the self-dual codes over R are the self-dual codes over F2, and based on the Mac Williams identities for the Hamming weight enumerators of linear codes over F2, the Mac Williams identities for Lee weight enumerators of linear codes over R are given. Further, by introducing a special variable t, the Mac Williams identities for the complete weight enumerators of linear codes over R are obtained. Finally, an example which illustrates the correctness and function of the two Mac Williams identities is provided.展开更多
In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee ...In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee weight for linear codes over F2m ＋ uF2m. Furthermore, the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.展开更多
基金supported by the Natural Science Foundation of Hubei Province under Grant No.D20144401the Natural Science Foundation of Hubei Polytechnic University under Grant Nos.12xjz14A,11yjz37B
文摘The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F2 ＋ u F2 ＋ v F2 are defined and Gray map from R^nto F2^3n is constructed. By proving the fact that the Gray images of the self-dual codes over R are the self-dual codes over F2, and based on the Mac Williams identities for the Hamming weight enumerators of linear codes over F2, the Mac Williams identities for Lee weight enumerators of linear codes over R are given. Further, by introducing a special variable t, the Mac Williams identities for the complete weight enumerators of linear codes over R are obtained. Finally, an example which illustrates the correctness and function of the two Mac Williams identities is provided.
基金supported by National Natural Science Funds of China under Grant No.60973125College Doctoral Funds of China under Grant No.20080359003+1 种基金Anhui College Natural Science Research Project under Grant No.KJ2010B171Research Project of Hefei Normal University under Grant No.2012kj10
文摘In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee weight for linear codes over F2m ＋ uF2m. Furthermore, the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.
