Transitive and self-dual codes attaining the Tsfasman-Vlǎduţ-Zink bound

IEEE Transactions on Information Theory

Volumn 52, Issue 5, 2006, Pages 2218-2224

  Stichtenoth, Henning ^a,b  

^a SABANCI UNIVERSITY   (Turkey)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Asymptotically good codes; Cyclic codes; Self dual codes; Towers of function fields; Transitive codes; Tsfasman Vl du Zink bound

Indexed keywords

ASYMPTOTIC STABILITY; CODES (SYMBOLS); ENCODING (SYMBOLS); FUNCTIONS;

ASYMPTOTICALLY GOOD CODES; CODING THEORY; CYCLIC CODES; FUNCTION FIELDS; GILBERT-VARSHAMOV BOUND; SELF-DUAL CODES; TRANSITIVE CODES;

INFORMATION THEORY;

EID: 33646054110     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.872986     Document Type: Article

References (22)

1. N. Elkies, "Excellent nonlinear codes from modular curves," in STOC' 01: Proc. 33rd Annu. ACM Symp. Theory Comput., Hersonissos, Greece, pp. 200-208.
2. N. Elkies, "Still Better Nonlinear Codes from Modular Curves," arXiv:mAth.NT/0308046, 2003.
3. G. Frey, M. Perret, and H. Stichtenoth, "On the different of Abelian extensions of global fields," in Coding Theory and Algebraic Geometry, H. Stichtenoth and M. A. Tsfasman, Eds. New York: Springer, 1992, vol. LNM 1518, Lecture Notes in Mathematics, pp. 26-32.
4. A. Garcia and H. Stichtenoth, "A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound," Invent. Math., vol. 121, pp. 211-222, 1995.
5. A. Garcia and H. Stichtenoth, "On the asymptotic behavior of some towers of function fields over finite fields," J. Number Theory, vol. 61, pp. 248-273, 1996.
6. A. Garcia and H. Stichtenoth, "Some Artin-Schreier towers are easy," Moscow Math. J., to be published.
7. Y. Ihara, "Some remarks on the number of rational points of algebraic curves over finite fields," J. Fac. Sci. Univ. Tokyo, vol. 28, pp. 721-724, 1981.
8. J. H. van Lint, Introduction to Coding Theory. New York: Springer-Verlag, 1982.
9. 2?," J. Fac. Sci. Univ. Tokyo, vol. 28, pp. 715-720, 1981.
10. C. Martinez-Perez and W. Willems, "Is the class of cyclic codes good?," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 696-700, Feb. 2006, to be published.
11. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
12. H. Niederreiter and F. Özbudak, "Constructive asymptotic codes with an improvement on the Tsfasman-Vlǎduţ-Zink and Xing bound," in Coding, Cryptography and Combinatorics, K. Q. Feng, H. Niederreiter, and C. P. Xing, Eds. Basel: Birkhäuser, 2004, vol. 23, Progress in Computer Science and Applied Logic, pp. 259-275.
13. H. Niederreiter and F. Özbudak, "Further Improvements on Asymptotic Bounds for Codes using Distinguished Divisors," preprint, 2005.
14. H. Niederreiter and C. P. Xing, Rational Points on Curves over Finite Fields. Cambridge: Cambridge Univ. Press, 2001.
15. Handbook of Coding Theory, vol. I and II, V. S. Pless and W. C. Huffmann, Eds., Elsevier, Amsterdam, The Netherlands, 1998.
16. W. Scharlau, "Selbstduale Goppa-codes," Math. Nachr., vol. 143, pp. 119-122, 1989.
17. H. Stichtenoth, Algebraic Function Fields and Codes. Berlin, Germany: Springer-Verlag, 1993.
18. H. Stichtenoth, "Self-dual Goppa codes," J. Pure Appl. Algebra, vol. 55, pp. 199-211, 1988.
19. H. Stichtenoth and C. P. Xing, "Excellent nonlinear codes from algebraic function fields," IEEE Trans. Inf. Theory, vol. 51, no. 11, pp. 4044-4046, Nov. 2005.
20. M. A. Tsfasman and S. G. Vlǎduţ, Algebraic-Geometric Codes. Dordrecht, The Netherlands: Kluwer, 1991.
21. M. A. Tsfasman, S. G. Vlǎduţ, and T. Zink, "Modular curves, Shimura curves, and Goppa codes better than the Varshamov-Gilbert bound," Math. Nachr., vol. 109, pp. 21-28, 1982.
22. C. P. Xing, "Nonlinear codes from algebraic curves improving the Tsfasman-Vlǎduţ-Zink bound," IEEE Trans. Inf. Theory, vol. 49, pp. 1653-1657, Jul. 2003.