Decoding of Codes Defined by a Single Point on a Curve

IEEE Transactions on Information Theory

Volumn 41, Issue 6, 1995, Pages 1709-1719

  O'Sullivan, Michael E ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Algebraic geometry codes; Berlekamp Massey algorithm; decoding

Indexed keywords

EID: 0001144118     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.476244     Document Type: Article

References (20)

1. C. Dahl, “Fast decoding of codes from algebraic curves,” IEEE Trans. Inform. Theory, vol. 40, pp. 223–229, Jan. 1994.
2. I. M. Duursma, “Algebraic decoding using special divisors,” IEEE Trans. Inform. Theory, vol. 39, pp. 694–698, Mar. 1993.
3. —, “Majority coset decoding,” IEEE Trans. Inform. Theory, vol. 39, pp. 1067–1070, May 1993.
4. D. Ehrhard, “Achieving the designed error capacity in decoding algebraic-geometric codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 743–751, Mar. 1993.
5. G. L. Feng and T. R. N. Rao, “Decoding algebraic-geometry codes up to the designed minimum distance,” IEEE Trans. Inform. Theory, vol. 39, pp. 37–45, Jan. 1993.
6. A. Garcia, S. J. Kim, and R. Lax, “Consecutive Weierstrass gaps and minimum distance of Goppa codes,” J. Pure Appl. Algebra, vol. 84, pp. 199–207, Feb. 3, 1993.
7. J. Justesen, K. Larsen, A. Havemose, H. E. Jensen, and T. Høholdt, “Construction and decoding of a class of algebraic geometry codes,” IEEE Trans. Inform. Theory, vol. 35, pp. 811–821, July 1989.
8. J. Justesen, K. Larsen, H. E. Jensen, and T. Høholdt, “Fast decoding of codes from algebraic plane curves,” IEEE Trans. Inform. Theory, vol. 38, pp. 111–119, Jan. 1992.
9. R. Pellikaan, “On a decoding algorithm for codes on maximal curves,” IEEE Trans. Inform. Theory, vol. 35, pp. 1228–1232, Nov. 1989.
10. —, “On the efficient decoding of algebraic-geometric codes,” in Proc.: Eurocode 1993.
11. R. Pellikaan and C. Kirfel, “The minimum distance of codes in an array coming from telescopic semigroups,” Eindhoven, The Netherlands, May 1993.
12. S. C. Porter, B. Z. Shen, and R. Pellikaan, “Decoding geometric Goppa codes using an extra place,” IEEE Trans. Inform. Theory, vol. 38, pp. 1663–1676, Nov. 1992.
13. S. Sakata, “Extension of the Berlekamp-Massey algorithm to N dimensions,” Inform. Comput. vol. 84, pp. 207–239, Feb. 1990.
14. —, “Decoding binary 2D cyclic codes by the 2D Berlekamp-Massey algorithm,” IEEE Trans. Inform. Theory, vol. 37, pp. 1200–1203, July 1991.
15. S. Sakata, J. Justesen, Y. Madelung, H. E. Jensen, and T. Høholdt, “Fast decoding of AG-codes up to the designed minimum distance,” IEEE Trans. Inform. Theory, this issue, pp. 1672–1677.
16. S. Sakata, J. Justesen, Y. Madelung, H. E. Jensen, and T. Høholdt, “A fast decoding method of AG codes from Miura-Kamiya curves Cab up to half the Feng-Rao bound,” Finite Fields and Applications, vol. 1, no. 1, to be published.
17. A. N. Skorobogatov and S. G. Vladut, “On the decoding of algebraic-geometric codes,” IEEE Trans. Inform. Theory, vol. 36, pp. 1051–1060, Sept. 1990.
18. H. Stichtenoth, Algebraic Function Fields and Codes. Berlin, Germany: Springer-Verlag Universitext, 1993.
19. N. Stichtenoth, “A note on Hermitian curves over GF(q2),” it IEEE Trans. Inform. Theory, vol. 37, pp. 1345–1348, Sept. 1991.
20. K. C. Yang and P. V. Kumar, “On the true minimum distance of Hermitian codes,” in Coding Theory and Algebraic Geometry-Proc., Luminy, 1991, H. Stichtenoth and M. A. Tsfasman, Eds. Berlin, Germany: Springer Lect. Notes Math. no. 1518, 1992, pp. 99–107.