On the equivalence of NMDS codes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914123232575488 |
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| author | Lu, Jianbing Zhou, Yue |
| author_facet | Lu, Jianbing Zhou, Yue |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25645 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the equivalence of NMDS codes Lu, Jianbing Zhou, Yue Information Theory 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. |
| title | On the equivalence of NMDS codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2509.25645 |