Abstract
The Lee weight enumerators and the complete weight enumerators for the linear codes over ring R = F 2 + uF 2 + vF 2 are defined and Gray map φ from R n to F 3n2 is constructed. By proving the fact that the Gray images of the self-dual codes over R are the self-dual codes over F 2, and based on the MacWilliams identities for the Hamming weight enumerators of linear codes over F 2, the MacWilliams identities for Lee weight enumerators of linear codes over R are given. Further, by introducing a special variable t, the MacWilliams 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 MacWilliams identities is provided.
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This research was supported by the Natural Science Foundation of Hubei Province under Grant No. D20144401 and the Natural Science Foundation of Hubei Polytechnic University under Grant Nos. 12xjz14A, 11yjz37B.
This paper was recommended for publication by Editor HU Lei.
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Liu, X., Liu, H. Macwilliams identities of linear codes over the ring F 2 + uF 2 + vF 2 . J Syst Sci Complex 28, 691–701 (2015). https://doi.org/10.1007/s11424-015-2246-x
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DOI: https://doi.org/10.1007/s11424-015-2246-x