Rational points, genus and asymptotic behaviour in reduced algebraic curves over finite fields

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134386The number A(q) shows the asymptotic behaviour of the quotient of the number of rational points over the genus of non-singular absolutely irreducible curves over a finite field Fq. Research on bounds for A(q) is closely connected with the so-called asymptotic main problem in Coding Theory. In this paper, we study some generalizations of this number for non-irreducible curves, their connection with A(q) and its application in Coding Theory.8 pagesAlgebraic GeometryInformation TheoryNumber Theory14Q05Rational points, genus and asymptotic behaviour in reduced algebraic curves over finite fieldstext