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Constructions of near MDS codes which are optimal locally recoverable codes.

Authors :
Li, Xiaoru
Heng, Ziling
Source :
Finite Fields & Their Applications. Jun2023, Vol. 88, pN.PAG-N.PAG. 1p.
Publication Year :
2023

Abstract

A linear code with length n , dimension k and minimum distance n − k is said to be almost maximum distance separable (AMDS for short). An AMDS code whose dual is also AMDS is referred to as a near maximum distance separable (NMDS for short) code. NMDS codes have nice applications in finite geometry, combinatorics, cryptography and data storage. In this paper, we first present several constructions of NMDS codes and determine their weight enumerators. In particular, some constructions produce NMDS codes with the same parameters but different weight enumerators. Then we determine the locality of the NMDS codes and obtain many families of distance-optimal and dimension-optimal locally recoverable codes. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10715797
Volume :
88
Database :
Academic Search Index
Journal :
Finite Fields & Their Applications
Publication Type :
Academic Journal
Accession number :
162937898
Full Text :
https://doi.org/10.1016/j.ffa.2023.102184