Abstract
In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over \(\mathbb{F}_2 + u\mathbb{F}_2\) is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee weight for linear codes over \(\mathbb{F}_{2^m } + u\mathbb{F}_{2^m }\). Furthermore, the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.
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This research is supported by National Natural Science Funds of China under Grant No. 60973125, College Doctoral Funds of China under Grant No. 20080359003, Anhui College Natural Science Research Project under Grant No. KJ2010B171, and Research Project of Hefei Normal University under Grant No. 2012kj10.
This paper was recommended for publication by Editor Xiao-Shan GAO.
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Zhu, S., Tang, Y. A MacWilliams type identity on Lee weight for linear codes over \(\mathbb{F}_2 + u\mathbb{F}_2^*\) . J Syst Sci Complex 25, 186–194 (2012). https://doi.org/10.1007/s11424-012-9219-0
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DOI: https://doi.org/10.1007/s11424-012-9219-0