A MacWilliams type identity on Lee weight for linear codes over \mathbb{F}_2 + u\mathbb{F}_2^* |
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| Authors: | Shixin Zhu Yongsheng Tang |
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| Institution: | 1. School of Mathematics, Hefei University of Technology, Hefei, 230009, China
2. Department of Mathematics, HeFei Normal University, Hefei, 230601, China
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| Abstract: | In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over
\mathbbF2 + u\mathbbF2\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
\mathbbF2m + u\mathbbF2m \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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