A theorem about linear rank inequalities that depend on the characteristic of the finite field

• Autor: Peña Macias, Victor
• Formato: artículo
• Fecha de Publicación: 2022
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: inglés
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/4177
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/4177
• Nivel de acceso: acceso abierto
• Materia: Mutually complementary vector spaces; Binary matrix; Finite field; Entropy; Linear rank inequality; Espacios vectoriales mutuamente complementarios; Matriz binaria; Cuerpo finito; Entropía; Desigualdad rango lineal

A linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over finite fields of determined characteristics, and does not in general hold over other characteristics. In this paper, using as guide binary matrices whose ranks depend on the finite field where they are defined, we show a theorem which explicitly produces characteristic-dependent linear rank inequalities; this theorem generalizes results previously obtained in the literature.