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arXiv · 2406.18307

Five-Lee-weight linear codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$

Pavan Kumar·Noor Mohammad Khan
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Abstract

In this study, linear codes having their Lee-weight distributions over the semi-local ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$ with $u^{2}=1$ are constructed using the defining set and Gauss sums for an odd prime $q $. Moreover, we derive complete Hamming-weight enumerators for the images of the constructed linear codes under the Gray map. We finally show an application to secret sharing schemes.

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Pavan Kumar, Noor Mohammad Khan. 2024-06-26. Five-Lee-weight linear codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$. https://arxiv.org/abs/2406.18307

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