Bases for Riemann-Roch spaces of one-point divisors on an optimal tower of function fields

IEEE Transactions on Information Theory

Volumn 58, Issue 5, 2012, Pages 2589-2598

  Noseda, Francesco ^a   Oliveira, Gilvan ^b   Quoos, Luciane ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b FEDERAL UNIVERSITY OF ESPÍRITO SANTO   (Brazil)

Author keywords

Algebraic geometric codes; Riemann Roch spaces; tower of function fields; Weierstrass semigroup

Indexed keywords

ALGEBRAIC GEOMETRIC CODES; FINITE FIELDS; FUNCTION FIELDS; RIEMANN-ROCH SPACE; SEMIGROUPS; WEIERSTRASS SEMIGROUP;

ALGEBRA;

OPTIMIZATION;

EID: 84860248506     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2179519     Document Type: Article

References (14)

1. A. Garcia and J. Bezerra, "A tower with non-Galois steps which attains the Drinfeld-Vľaduţbound," J. Number Theory, vol. 106, no. 1, pp. 142-154, 2004.
2. A. Garcia and H. Stichtenoth, "A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vľaduţbound," Invent. Math., vol. 121, pp. 211-222, 1995.
3. A. Garcia and H. Stichtenoth, "On tame towers over finite fields," J. Reine Angew. Math., vol. 557, pp. 53-80, 2003.
4. A. Garcia and H. Stichtenoth, "Explicit towers of function fields over finite fields," in Topics in Geometry, Coding Theory and Cryptography. New York: Springer-Verlag, 2007, pp. 1-58.
5. X. Hu and H. Maharaj, "On the qth power algorithm," Finite Fields Appl., vol. 14, pp. 1068-1082, 2008.
6. W.-C. W. Li, H. Maharaj, H. Stichtenoth, and N. D. Elkies, "New optimal tame towers of function fields over small finite fields," in Algorithmic Number Theory, ser. Lecture Notes in Computer Science. New York: Springer-Verlag, 2002, vol. 2369, pp. 372-389.
7. H. Maharaj, "Code construction on fiber products of Kummer curves," IEEE Trans. Inf. Theory, vol. 50, no. 9, pp. 2169-2173, Sep. 2004.
8. H. Maharaj, "Explicit constructions of algebraic-geometric codes," IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 714-722, Feb. 2005.
9. R. Pellikaan, H. Stichtenoth, and F. Torres, "Weierstrass semigroups in an asymptotically good tower of function fields," Finite Fields Appl., vol. 4, pp. 381-392, 1998.
10. W. K. Shum, I. Aleshnikov, P. V. Kumar, H. Stichtenoth, and V. Deolalikar, "A low complexity algorithm for the construction of algebraic-geometric codes better than the Gilbert-Varshamov bound," IEEE Trans. Inf. Theory, vol. 47, no. 6, pp. 2225-2241, Sep. 2001.
11. H. Stichtenoth, Algebraic Function Fields and Codes, 2nd ed. New York: Springer-Verlag, 2009.
12. G. D. Villa Salvador, Topics in the Theory of Algebraic Function Fields. Cambridge, MA: Birkhäuser, 2006.
13. S. G. Vľaduţand V. G. Drinfeld, "Number of points of an algebraic curve," Funct. Anal. Appl., vol. 17, pp. 53-54, 1983.
14. C. C. Voss and T. Høholdt, "An explicit construction of a sequence of codes attaining the Tsfasman-Vľaduţ-Zink bound. The first steps," IEEE Trans. Inf. Theory, vol. 43, no. 1, pp. 128-135, Jan. 1997.