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 Isomorphism classes of genus-3 pointed trigonal curves over finite fields of characteristic $2$ Bull. Korean Math. Soc. 2009 Vol. 46, No. 5, 917-930 https://doi.org/10.4134/BKMS.2009.46.5.917Printed September 1, 2009 Pyung-Lyun Kang and Sunmi Sun Chungnam National University and Daejeon Gwanjeo High School Abstract : We find all distinct representatives of isomorphism classes of genus-3 pointed trigonal curves and compute the number of isomorphism classes of a special class of genus-3 pointed trigonal curves including that of Picard curves over a finite field $F$ of characteristic $2$. Keywords : isomorphism classes, genus-$3$ trigonal curves, Picard curve, finite fields of characteristic $2$ MSC numbers : 11G20 Downloads: Full-text PDF