2024/06/19 by Umberto Martínez-Peñas, Martínez-Peñas, Umberto, Rubén Rodríguez-Ballesteros +1 · 2 citations
Computer Science · Engineering · #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2406.13355
openalex publication_date 2024/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 sizes. We provide explicit examples and a binary construction with optimal lengths relative to their field sizes, which beats any MDS code.