On Chebyshev polynomials and maximal curves

Arnaldo Garcia, Henning Stichtenoth
1999 Acta Arithmetica  
1. Introduction. The interest in curves (projective, nonsingular and geometrically irreducible) over finite fields with many rational points was renewed after Goppa's construction of codes from curves. Particularly interesting is the case of maximal curves over K = F q 2 , i.e., curves C defined over K such that the number #C(K) of K-rational points attains the Hasse-Weil upper bound:
doi:10.4064/aa-90-4-301-311 fatcat:xrk2m2kcvjhjhpahabptbftkoy