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arXiv · 2304.04176

A Proof of a Conjecture About a Class of Near Maximum Distance Separable Codes

Wei Lu·Xia Wu
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Abstract

In this paper, we completely determine the number of solutions to $ \operatorname{Tr}^{q^2}_q(bx+b)+c=0, x\in μ_{q+1}\backslash \{-1\}$ for all $b\in \mathbb{F}_{q^2}, c\in\mathbb{F}_{q}$. As an application, we can give the weight distributions of a class of linear codes, and give a completely answer to a recent conjecture about a class of NMDS codes proposed by Heng.

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Wei Lu, Xia Wu. 2023-04-09. A Proof of a Conjecture About a Class of Near Maximum Distance Separable Codes. https://arxiv.org/abs/2304.04176

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