Explicit constructions of algebraic-geometric codes

IEEE Transactions on Information Theory

Volumn 51, Issue 2, 2005, Pages 714-722

  Maharaj, Hiren ^a  

^a CLEMSON UNIVERSITY   (United States)

Author keywords

Algebraic geometric codes; Explicit constructions; Goppa codes

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; POLYNOMIALS;

ALGEBRAIC GEOMETRIC CODES; EXPLICIT CONSTRUCTIONS; GOPPA CODES;

CODES (SYMBOLS);

EID: 13444280302     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.840896     Document Type: Article

References (18)

1. I. Aleshnikov. V. Deolalikar, P. V. Kumar, and H. Stichtenoth, "Toward a basis for the space of regular functions in a tower of function fields meeting the Drinfeld-Vladut bound," in Proc. 5th Int Conf. Finite Fields and Applications, Augsburg, Germany, Aug. 1999.
2. P. Beelen and R. Pellikaan, "The Newton polygon of plane curves with many rational points," Des., Codes Cryptogr., vol. 21. no. 1-3, pp. 41-67, 2000.
3. M. Daberkow, C. Fieker, J. Klüners, M. Pohst, K. Roegner, and K.Wildanger, "KANT V4," J. Symbol. Comp., vol. 24, pp. 267-283, 1997.
4. D. A. Leonard, "Finding the defining functions for one-point algebraic-geometry codes,"IEEE Trans. Inf. Theory, vol. 47, no. 6, pp. 2566-2573, Sep. 2001.
5. D. A. Leonard and R. Pellikaan, "Integral closures and weight functions over finite fields," Finite Fields Appl., vol. 9, no. 4, pp. 479-504, 2003.
6. H. Maharaj, "Code construction on fiber products of Kummer covers," IEEE Trans. Inf. Theory, vol. 50, no. 9, pp. 2169-2173, Sep. 2004.
7. H. Maharaj, "Explicit constructions of algebraic-geometric codes from towers," manuscript in review.
8. H. Maharaj, "Explicit Goppà Code construction on fiber products of Kummer covers using differentials," manuscript in review.
9. H. Maharaj, "Explicit constructions of algebraic geometric codes using differentials," manuscript in review.
10. H. Maharaj, "Improved tower bounds of the minimum distance of a class of Goppa codes," manuscript in review.
11. H. Niederreiter and C. P. Xing, "Cyclotomic function fields, Hilbert class fields, and global function fields with many rational places," Acta Arithm., vol. 79, pp. 59-76, 1997.
12. H. Niederreiter and C. P. Xing, Rational Points on Curves over Finite Fields. Cambridge, U.K.: Cambridge Univ. Press, 2001. vol. 285. London Math. Soc. Lecture Note Ser..
13. 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.
14. K. W. Shum, I. AIeshnikov, P. V. Kumar, H. Stichtenoth, and V. Deolalikar, "A low-complexity algorithm for the constraction of algebraic-geometric codes better than the Gilbert-Varshamov bound," IEEE Trans. Inf. Theory, vol. 47, no. 6, pp. 2225-2241, Sep. 2001
15. H. Stichtenoth, Algebraic Function Fields and Codes, Berlin, Germany: Springer-Verlag, 1993.
16. G. van der Geer and M. van der Vlugt, "How to construct curves over finite fields with many points," in Arithmetic Geometry, vol. XXXVII, Sympos. Math., Cortona, 1994, pp. 169-189.
17. G. van der Geer and van der Vlught, "Tables of curves with many points," Math. Comput., vol. 69, no. 230, pp. 797-810, 2000.
18. C. P. Xing, "Hyperelliptic function fields and codes," J. Pure Appl. Alg., vol. 74, no. 1, pp. 109-118, 1991.