2025/12/01 by Cristina Fernández-Córdoba, Fernández-Córdoba, Cristina, Sergi Sánchez-Aragón +3
Computer Science · Engineering · Mathematics · #94B05 #94B25 #94B60 #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2512.02149
openalex publication_date 2025/12/01 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28
A linear code of length n over a finite chain ring R with residue field \Fq is a R-submodule of Rn. A R-linear code is a code over \Fq (not necessarily linear) which is the generalized Gray map image of a linear code over R. These codes can be seen as a generalization of the linear codes over \Zps with p prime and s ≥ 1. In this paper, we present the construction of linear simplex codes over R and their corresponding R-linear simplex codes of type α and β. Moreover, we show the fundamental parameters of these codes, including their minimum Hamming distance, as well as their complete weight distributions. We also study whether these simplex codes are optimal with respect to the Griesmer-type bound.