[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2010.47.2.433

REMARKS ON THE GAP SET OF R = K + C

Tutas, Nesrin (DEPARTMENT OF MATHEMATICS AKDENIZ UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.47, no.2, 2010 , pp. 433-442 More about this Journal

Abstract

$\tilde{G}(P,\;Q)$ , a new generalization of the set of gap numbers of a pair of points, was described in [1]. Here we study gap numbers of local subring $R\;=\;\cal{K}\;+\;C$ of algebraic function field over a finite field and we give a formula for the number of elements of $\tilde{G}(P,\;Q)$ depending on pure gaps and R.

Keywords

Weierstrass points; gap numbers;

Citations & Related Records

Times Cited By Web Of Science : 0 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

Reference

1	M. Homma, The Weierstrass semigroup of a pair of points on a curve, Arch. Math. (Basel) 67 (1996), no. 4, 337–348. DOI ScienceOn
2	E. Kang and S. J. Kim, Special pairs in the generating subset of the Weierstrass semigroup at a pair, Geom. Dedicata 99 (2003), 167–177. DOI
3	H. I. Karakas, On Rosenlicht's generalization of Riemann-Roch theorem and generalized Weierstrass points, Arch. Math. (Basel) 27 (1976), no. 2, 134–147. DOI
4	H. I. Karakas, Application of generalized Weierstrass points: divisibility of divisor classes, J. Reine Angew. Math. 299/300 (1978), 388–395.
5	S. J. Kim, On the index of the Weierstrass semigroup of a pair of points on a curve, Arch. Math. (Basel) 62 (1994), no. 1, 73–82. DOI ScienceOn
6	G. Matthews, Weierstrass pairs and minimum distance of Goppa codes, Des. Codes Cryptogr. 22 (2001), no. 2, 107–121. DOI
7	G. Matthews, Codes from the Suzuki function field, IEEE Trans. Inform. Theory 50 (2004), no. 12, 3298–3302. DOI ScienceOn
8	M. Rosenlicht, Equivalence relations on algebraic curves, Ann. of Math. (2) 56 (1952), 169–191. DOI
9	A. Garcia and P. Viana, Weierstrass points on certain nonclassical curves, Arch. Math. (Basel) 46 (1986), no. 4, 315–322. DOI ScienceOn
10	P. Beelen and N. Tutas, A generalization of the Weierstrass semigroup, J. Pure Appl. Algebra 207 (2006), no. 2, 243–260. DOI ScienceOn
11	N. Tuta¸s, On Weierstrass point of semilocal subrings, JP J. Algebra Number Theory Appl. 13 (2009), no. 2, 221–235.
12	H. Stichtenoth, Algebraic Function Fields and Codes, Springer-Verlag, Berlin, 1993.