Abstract
Using two divisors F and D on an algebraic curve, Goppa [G] introduced a new way to construct a linear code, and he estimated the main parameters of the code. Choosing more restricted divisors F and D than ones in the general construction of a Goppa code, we may expect to improve the lower bound of the minimum distance. Actually, Garcia and Lax [GL] succeeded in improving the bound by taking F as a multiple mQ of a Weierstrass point Q with a coefficient m expressed in terms of two Weierstrass gaps at Q. Soon after the discovery, Garcia, Kim and Lax [GKL] showed that if the Weierstrass gaps at the point Q have consecutive integers, one can obtain a code which has rather greater minimum distance.
This work has been supported by the Japan Society for the Promotion of Science and the Korea Science and Engineering Foundation, Project No. 976–0100–001–2.
second author is partially supported by KOSEF-GARC and by the Basic Science Research Institute Program, Ministry of Education, Project No. BSRI-98–1406.
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© 2000 Kluwer Academic Publishers
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Homma, M., Kim, S.J. (2000). Goppa Codes Supported by Two Points on a Curvet. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0271-1_18
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DOI: https://doi.org/10.1007/978-1-4613-0271-1_18
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