Let F/IFq be a function field over a finite field ifq. We have seen in Chapter 5 that the number N of rational places of F over ifq satisfies the Hasse Weil Bound N ≤ q + 1 + 2gq1/2, and that this upper bound can be attained only if g ≤ (q − q1/2)/2. Here our aim is to investigate what happens if the genus is large with respect to q. The results of this chapter have interesting applications in coding theory, see Section 8.4.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Asymptotic Bounds for the Number of Rational Places. In: Algebraic Function Fields and Codes. Graduate Texts in Mathematics, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76878-4_7
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DOI: https://doi.org/10.1007/978-3-540-76878-4_7
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