A generalized forney formula for algebraic-geometric codes

IEEE Transactions on Information Theory

Volumn 42, Issue 4, 1996, Pages 1263-1268

  Leonard, Douglas A ^a,b  

^a IEEE

^b AUBURN UNIVERSITY   (United States)

Author keywords

AG (algebraic geometric) codes; Error locator ideals; Forney formula; Gr bner bases

Indexed keywords

ALGORITHMS; CODING ERRORS; DECODING; ERROR ANALYSIS; ERROR DETECTION; FUNCTIONS; GEOMETRY; INFORMATION THEORY; MATHEMATICAL MODELS; POLYNOMIALS;

ALGEBRAIC GEOMETRY CODES; ERROR LOCATOR IDEALS; GENERALIZED FORNEY FORMULA; GROBNER BASIS; LATTICE SHIFTING; ROW REDUCTION ALGORITHMS; WEIGHTED TOTAL DEGREE MONOMIAL ORDERING;

CODES (SYMBOLS);

EID: 0030195163     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.508855     Document Type: Article

References (19)

1. D. Cox, J. Little, and D. O'Shea, Ideals, Varieties, and Algorithms. New York: Springer-Verlag, 1992.
2. C. Dahl, "Fast decoding of codes from algebraic curves," IEEE Trans. Inform. Theory, vol. 40, pp. 223-229, 1994.
3. I. Duursma, "Decoding codes from curves and cyclic codes," Ph.D. dissertation, Eindhoven University of Technology, Findhoven, The Netherlands, Sept. 1993.
4. D. Erhard, "Decoding algebraic-geometric codes by solving a key equation," in Proc. AGCT-3, H. Stichtenoth and M. Tsfasman, Eds. New York: Springer LNM 1518, 1992.
5. G.-L. Feng and T. R. N. Rao, "Decoding of algebraic-geometric codes up to the designed minimum distance," IEEE Trans. Inform. Theory, vol. 39, 1993.
6. G.-L. Feng, V. K. Wei, T. R. N. Rao, and K. K. Tzeng, "Simplified understanding and efficient decoding of a class of algebraic-geometric codes," IEEE Trans. Inform. Theory, vol. 40, pp. 981-1002, July 1994.
7. G. D. Forney, "On decoding BCH codes," IEEE Trans. Inform. Theory, vol. IT-10, pp. 549-557, Mar. 1965.
8. D. Gruntz, "Groebner bases in Gauss," MapleTech, vol. 9, 1993.
9. J. Justesen, K. J. Larsen, H. Elbrønd Jensen, and T. Hohøldt, "Fast decoding of codes from algebraic plane curves," IEEE Trans. Inform. Theory, vol. 38, pp. 111-119, Jan. 1992.
10. D. A. Leonard, "Error-locator ideals for algebraic-geometric codes," IEEE Trans. Inform. Theory, vol. 41, pp. 819-823, May 1995.
11. B. Mishra, Algorithmic Algebra (Texts and Monographs in Computer Science). New York: Springer-Verlag, 1993.
12. M. E. O'Sullivan, "Decoding of codes defined by a single point on a curve," IEEE Trans. Inform. Theory, vol. 41, no. 6, pp. 1709-1719, Nov. 1995.
13. R. Pellikaan, "On the efficient decoding of algebraic-geometric codes," in Proc. Eurocode92, CISM Courses and Lectures, vol. 339. Wien, New York: Springer-Verlag, 1993, pp. 231-253.
14. 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, 1992.
15. K. Saints and C. Heegard, "Algebraic-geometric codes and multidi mensional cyclic codes: A unified theory and algorithms for decoding using Gröbner bases," IEEE Trans. Inform. Theory, vol. 41, no. 6, pp. 1733-1751, Nov. 1995.
16. S. Sakata, "Finding a minimal set of linear recurring relations capable of generating a two-dimensional array," J. Symb. Comput., vol. 5, pp. 321-327, 1988.
17. _, "Extension of Berlekamp-Massey algorithm to N dimensions," Inform. Comput., vol. 84, pp. 207-239, 1990.
18. S. Sakata, J. Justesen, Y. Madelug, H. Elbrønd Jensen, and T. Hohøldt, "Fast decoding of AG-codes up to the designed minimum distance," IEEE Trans. Inform. Theory, vol. 41, no.6, pp. 1672-1677, Nov. 1995.
19. B.-Z. Shen, "On encoding and decoding of the codes from Hermitian curves," in Cryptography and Coding III, M. Ganley Ed. London, UK: Oxford Univ. Press, to appear.