2024/02/06 by José Joaquín Bernal, Bernal, José Joaquín, Diana H. Bueno-Carreño +3 · 1 citation
Computer Science · Engineering · #Advanced Control Systems Design #FOS: Computer and information sciences #Fuzzy Logic and Control Systems #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2402.03938
openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to studying two main problems: 1) computing the apparent distance of an Abelian code and 2) giving a notion of Bose, Ray-Chaudhuri, Hocquenghem (BCH) multivariate code. To do this, we first strengthen the notion of an apparent distance by introducing the notion of a strong apparent distance; then, we present an algorithm to compute the strong apparent distance of an Abelian code, based on some manipulations of hypermatrices associated with its generating idempotent. Our method uses less computations than those given by Camion and Sabin; furthermore, in the bivariate case, the order of computation complexity is reduced from exponential to linear. Then, we use our techniques to develop a notion of a BCH code in the multivariate case, and we extend most of the classical results on cyclic BCH codes. Finally, we apply our method to the design of Abelian codes with maximum dimension with respect to a fixed apparent distance and a fixed length.