RT info:eu-repo/semantics/article
T1 Linear codes in the folded Hamming distance and the quasi MDS property
A1 Martínez Peñas, Umberto
A1 Rodríguez Ballesteros, Rubén
K1 Códigos aditivos
K1 Geometría finita
K1 Distancia de Hamming plegada
K1 Códigos MDS
K1 Códigos polinómicos ideales
K1 Distribuciones de peso
AB In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define quasi MDS (QMDS) codes and dually QMDS codes, which attain a more relaxed variant of the classical Singleton bound. We provide several general results concerning these codes, including restriction, shortening, weight distributions, existence, density, geometric description and bounds on their lengths relative to their field or alphabet sizes. We provide explicit examples and a binary construction with optimal lengths relative to their field or alphabet sizes, which beats any MDS code (in terms of length compared to the field or alphabet size).
PB Springer Nature
SN 0925-1022
YR 2025
FD 2025
LK https://uvadoc.uva.es/handle/10324/79159
UL https://uvadoc.uva.es/handle/10324/79159
LA eng
NO Designs, Codes and Cryptography, 2025.
NO Producción Científica
DS UVaDOC
RD 21-nov-2025