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

Wei Lu; Xia Wu

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

Information Theory 2023-04-11 v1 math.IT

Authors: Wei Lu , Xia Wu

Abstract

In this paper, we completely determine the number of solutions to $\operatorname{Tr}^{q^2}_q(bx+b)+c=0, x\in \mu_{q+1}\backslash \{-1\}$ 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.

Keywords

near maximum distance separable codes linear codes weight distribution trace function conjecture finite fields

Cite

@article{arxiv.2304.04176,
  title  = {A Proof of a Conjecture About a Class of Near Maximum Distance Separable Codes},
  author = {Wei Lu and Xia Wu},
  journal= {arXiv preprint arXiv:2304.04176},
  year   = {2023}
}

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15 pages

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

Abstract

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