On the equivalence of NMDS codes

2025/09/30 by Lu, Jianbing, Zhou, Yue
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2509.25645

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 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.

Citations

• Near-MDS Codes from Maximal Arcs in PG(2,q)
• A construction of optimal locally recoverable codes
• Constructions of near MDS codes which are optimal locally recoverable codes
• On near-MDS codes and caps
• Near MDS codes from oval polynomials
• On planes through points off the twisted cubic in PG(3,q) and multiple covering codes
• On sets of vectors of a finite vector space in which every subset of basis size is a basis II

Related

• Near-MDS Codes from Maximal Arcs in PG(2,q)
• Constructions of near MDS codes which are optimal locally recoverable codes
• The extended codes of a family of reversible MDS cyclic codes
• New MDS codes of non-GRS type and NMDS codes
• Two classes of NMDS codes from Roth-Lempel codes