On the equivalence of NMDS codes

Jianbing Lu; Yue Zhou

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arXiv · 2509.25645

On the equivalence of NMDS codes

Jianbing Lu·Yue Zhou

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Abstract

An $[n,k,d]$ linear code is said to be maximum distance separable (MDS) or almost maximum distance separable (AMDS) if $d=n-k+1$ or $d=n-k$, respectively. If a code and its dual code are both AMDS, then the code is said to be near maximum distance separable (NMDS). For $k=3$ and $k=4$, there are many constructions of NMDS codes by adding some suitable projective points to arcs in $\mathrm{PG}(k-1,q)$. In this paper, we consider the monomial equivalence problem for some NMDS codes with the same weight distributions and present new constructions of NMDS codes.

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Jianbing Lu, Yue Zhou. 2025-09-30. On the equivalence of NMDS codes. https://arxiv.org/abs/2509.25645

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