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Isomorphism classes of genus-3 pointed trigonal curves over finite fields of characteristic 2

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초록

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.

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.

참고문헌 (9)

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  4. S. D. Galbraith, "Arithmetic on superelliptic curves", Math. Comp, 71(237), pp.393~405 (2002)
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  8. S. Miura, "Algebraic geometric codes on certain plane curves", Trans. IEICE, J75-A(11), pp.1735~1745 (1992)
  9. E. Nart, "Non-hyperelliptic curves of genus three over finite fields of characteristic two", J. Number Theory, 116(2), pp.443~473 (2006)

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