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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