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ISOMORPHISM CLASSES OF GENUS-3 POINTED TRIGONAL CURVES OVER FINITE FIELDS OF CHARACTERISTIC 2
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 Title & Authors
ISOMORPHISM CLASSES OF GENUS-3 POINTED TRIGONAL CURVES OVER FINITE FIELDS OF CHARACTERISTIC 2
Kang, Pyung-Lyun; Sun, Sun-Mi;
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 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;
 Language
English
 Cited by
 References
1.
S. Arita, Algorithms for computations in Jacobian group of Cab curve and their application to discrete-log based public key cryptosystems, IEICE Transactions J82-A (1999), no. 8, 1291–1299

2.
Y. Choie and D. Yun, Isomorphism classes of hyperelliptic curves of genus 2 over Fq, In: Information Security and Privacy, ACISP 2002. LNCS, vol. 2384, pp. 190–202, Springer, Heidelberg, 2002

3.
I. H. Encinas, A. J. Menezes, and J. M. Masqu´e, Isomorphism classes of genus-2 hyperelliptic curves over finite fields, AAECC 13 (2002), 57–65

4.
S. D. Galbraith, S. M. Paulus, and N. P. Smart, Arithmetic on superelliptic curves, Math. Comp. 71 (2002), no. 237, 393–405 crossref(new window)

5.
N. Koblitz, Hyperelliptic cryptosystems, J. Cryptology 1 (1989), no. 3, 139–150 crossref(new window)

6.
J. Lee, Isomorphism classes of Picard curves over finite fields, Appl. Algebra Engrg. Comm. Comput. 16 (2005), no. 1, 33–44 crossref(new window)

7.
R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Revision of the 1986 first edition. Cambridge University Press, Cambridge, 1994

8.
S. Miura, Algebraic geometric codes on certain plane curves, Trans. IEICE J75-A (1992), no. 11, 1735–1745

9.
E. Nart and C. Ritzenthaler, Non-hyperelliptic curves of genus three over finite fields of characteristic two, J. Number Theory 116 (2006), no. 2, 443–473 crossref(new window)