Linear codes with few weights over $\mathbb{F}_{p}+u\mathbb{F}_{p}$

Pavan Kumar; Noor Mohammad Khan

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arXiv · 2406.18325

Linear codes with few weights over $\mathbb{F}_{p}+u\mathbb{F}_{p}$

Pavan Kumar·Noor Mohammad Khan

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Abstract

For any positive integer $m$ and an odd prime $p$; let $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $q=p^{m}$, be a ring extension of the ring $\mathbb{F}_{p}+u\mathbb{F}_{p}.$ In this paper, we construct linear codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}$ by using trace function defined on $\mathbb{F}_{q}+u\mathbb{F}_{q}$ and determine their Hamming weight distributions by employing symplectic-weight distributions of their Gray images.

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Pavan Kumar, Noor Mohammad Khan. 2024-06-26. Linear codes with few weights over $\mathbb{F}_{p}+u\mathbb{F}_{p}$. https://arxiv.org/abs/2406.18325

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