Improved asymptotic bounds for codes using distinguished divisors of global function fields

SIAM Journal on Discrete Mathematics

Volumn 21, Issue 4, 2007, Pages 865-899

  Niederreiter, Harald ^a   Özbudak, Ferruh ^a,b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Asymptotic theory of codes; Gilbert Varshamov bound; Global function fields; Tsfasman Vl du ; Zink bound; Xing bound

Indexed keywords

ASYMPTOTIC ANALYSIS; CONTROL THEORY; PROBABILITY DENSITY FUNCTION;

ASYMPTOTIC BOUNDS; ASYMPTOTIC THEORIES; ASYMPTOTIC THEORY OF CODES; GILBERT-VARSHAMOV BOUND; GLOBAL FUNCTION FIELDS; GLOBAL FUNCTIONS; INFORMATION RATES; LINEAR CODES; LOWER BOUNDS; MINIMUM DISTANCES; XING BOUND;

CODES (SYMBOLS);

EID: 56649094579     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/060674478     Document Type: Article

References (14)

1. J. BEZERRA, A. GARCIA, AND H. STICHTENOTH, An explicit tower of function fields over cubic finite fields and Zink's lower bound, J. Reine Angew. Math., 589 (2005), pp. 159-199.
2. N. D. ELKIES, Excellent nonlinear codes from modular curves, in STOC'01, Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (Hersonissos, Greece, 2001), ACM Press, New York, 2001, pp. 200-208.
3. H. MAHARAJ, A note on further improvements of the TVZ-bound, IEEE Trans. Inform. Theory, 53 (2007), pp. 1210-1214.
4. H. NIEDERREITER AND F. ÖZBUDAK, Constructive asymptotic codes with an improvement on the Tsfasman- Vlǎduţ-Zink and Xing bounds, in Coding, Cryptography and Combinatorics K. Q. Feng, H. Niederreiter, and C. P. Xing, eds., Progr. Comput. Sci. Appl. Logic 23, Birkhäuser, Basel, 2004, pp. 259-275.
5. H. NIEDERREITER AND F. ÖZBUDAK, Further improvements on asymptotic bounds for codes using distinguished divisors, Finite Fields Appl., 13 (2007), pp. 423-443.
6. H. NIEDERREITER AND C. P. XING, Rational Points on Curves over Finite Fields: Theory and Applications, Cambridge University Press, Cambridge, UK, 2001.
7. H. STICHTENOTH, Algebraic Function Fields and Codes, Springer-Verlag, Berlin, 1993.
8. H. STICHTENOTH AND C. P. XING, Excellent nonlinear codes from algebraic function fields, IEEE Trans. Inform. Theory, 51 (2005), pp. 4044-4046.
9. M. A. TSFASMAN, Some remarks on the asymptotic number of points, in Coding Theory and Algebraic Geometry, H. Stichtenoth and M. A. Tsfasman, eds., Lecture Notes in Math. 1518, Springer, Berlin, 1992, pp. 178-192.
10. M. A. TSFASMAN AND S. G. VLǍDUŢ, Algebraic-Geometric Codes, Kluwer, Dordrecht, The Netherlands, 1991.
11. M. A. TSFASMAN, S. G. VLÄDUŢ, AND T. ZINK, Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound, Math. Nachr., 109 (1982), pp. 21-28.
12. S. G. VLǍDUŢ, An exhaustion bound for algebro-geometric "modular" codes, Problemy Peredachi Informatsii, 23 (1987), pp. 28-41.
13. C. P. XING, Algebraic-geometry codes with asymptotic parameters better than the Gilbert-Varshamov and the Tsfasman- Vlǎduţ-Zink bounds, IEEE Trans. Inform. Theory, 47 (2001), pp. 347-352.
14. C. P. XING, Nonlinear codes from algebraic curves improving the Tsfasman- Vlǎduţ-Zink bound, IEEE Trans. Inform. Theory, 49 (2003), pp. 1653-1657.