Affiliation:
1. Université Paris 8, Laboratoire de Géométrie, Analyse et Applications, LAGA Université Sorbonne Paris Nord, CNRS, UMR Villetaneuse France
2. Dipartimento di Matematica e Fisica Università degli Studi della Campania “Luigi Vanvitelli” Caserta Italy
Abstract
AbstractThe main purpose of this paper is to further study the structure, parameters and constructions of the recently introduced minimal codes in the sum‐rank metric. These objects form a bridge between the classical minimal codes in the Hamming metric, the subject of intense research over the past three decades partly because of their cryptographic properties, and the more recent rank‐metric minimal codes. We prove some bounds on their parameters, existence results, and, via a tool that we name geometric dual, we manage to construct minimal codes with few weights. A generalization of the celebrated Ashikhmin–Barg condition is proved and used to ensure the minimality of certain constructions.
Funder
Agence Nationale de la Recherche