`a`
Advances in Mathematics of Communications (AMC)
 

Weierstrass semigroup and codes over the curve $y^q + y = x^{q^r + 1}$
Pages: 67 - 72, Issue 1, February 2014

doi:10.3934/amc.2014.8.67      Abstract        References        Full text (303.9K)           Related Articles

Alonso Sepúlveda - Universidade Federal de Uberlandia, Campus Santa Monica, Av. Joao Naves de Avila, 2121, Uberlandia-MG, CEP 38.408-100, Brazil (email)
Guilherme Tizziotti - Universidade Federal de Uberlandia, Campus Santa Monica, Av. Joao Naves de Avila, 2121, Uberlandia-MG, CEP 38.408-100, Brazil (email)

1 E. Arbarello, M. Cornalba, P. Griffiths and J. Harris, Geometry of Algebraic Curves, Springer-Verlag, Berlin, 1985.       
2 E. Ballico, Weierstrass points and Weierstrass pairs on algebraic curves, Int. J. Pure Appl. Math., 2 (2002), 427-440.       
3 C. Carvalho and T. Kato, On Weierstrass semigroup and sets: a review with new results, Geom. Dedicata, 139 (2009), 139-195.       
4 I. M. Duursma, R. Kirov, Improved two-point codes on Hermitian curves, IEEE Trans. Inf. Theory, 57(7) (2011), 4469-4476.       
5 T. Hasegawa, S. Kondo and H. Kurusu, A sequence of one-point codes from a tower of function fields, Des. Codes Crypt., 41 (2006), 251-267.       
6 T. Høholdt, J. van Lint and R. Pellikaan, Algebraic Geometry Codes, Elsevier, 1998.       
7 M. Homma, The Weierstrass semigroup of a pair of points on a curve, Arch. Math., 67 (1996), 337-348.       
8 S. J. Kim, On index of the Weierstrass semigroup of a pair of points on a curve, Arch. Math., 62 (1994), 73-82.       
9 S. Kondo, T. Katagiri and T. Ogihara, Automorphism groups of one-point codes from the curves $y^q + y = x^{q^r+1}$, IEEE Trans. Inf. Theory, 47 (2001), 2573-2579.       
10 G. L. Matthews, Weierstrass pairs and minimum distance of Goppa codes, Des. Codes Crypt., 22 (2001), 107-121.       
11 G. L. Matthews, Codes from the Suzuki function field, IEEE Trans. Inf. Theory, 50(12) (2004), 3298-3302.       
12 C. Munuera, A. Sepulveda and F. Torres, Castle curve and codes, Adv. Math. Commun., 3 (2009), 399-408.       
13 H. Stichtenoth, Algebraic Function Fields and Codes, Springer, Berlin, 1993.       
14 M. Tsfasman, S. Vlădut and D. Nogin, Algebraic Geometric Codes: Basic Notions, Amer. Math. Soc., Providence, 2007.       
15 J. H. van Lint, Introduction to Coding Theory, Springer, New York, 1982.       

Go to top