Rational points, genus and asymptotic behaviour in reduced algebraic curves over finite fields
<|reference_start|>Rational points, genus and asymptotic behaviour in reduced algebraic curves over finite fields: The 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.<|reference_end|>
@article{farran1999rational,
    title={Rational points, genus and asymptotic behaviour in reduced algebraic
  curves over finite fields},
    author={J. I. Farran},
    journal={arXiv preprint arXiv:math/9910149},
    year={1999},
    number={AGT-34},
    archivePrefix={arXiv},
    eprint={math/9910149},
    primaryClass={math.AG cs.IT math.IT math.NT}
}