Hard problems of algebraic geometry codes

IEEE Transactions on Information Theory

Volumn 54, Issue 1, 2008, Pages 402-406

  Cheng, Qi ^a  

^a University of Oklahoma   (United States)

Author keywords

Algebraic geometric codes; Complexity theory; Maximum likelihood decoding

Indexed keywords

COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; DECODING; MAXIMUM LIKELIHOOD;

ALGEBRAIC-GEOMETRIC CODES; COMPLEXITY THEORY; MAXIMUM-LIKELIHOOD DECODING;

CODES (SYMBOLS);

EID: 38349185542     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2007.911213     Document Type: Article

References (15)

1. L. Adleman, "Algorithmic number theory - The complexity contribution," in Proc. 35th IEEE Symp. Found. Comp. Sci., 1994, pp. 88-113.
2. M. Altai, R. Kumar, and D. Sivakumar, "A sieve algorithm for the shortest lattice vector problem," in Proc. 33 th ACM Symp. Theory Comput., 2001, pp. 601-610.
3. E. R. Berlekamp, R. J. McEliece, and H. C. van Tilborg, "On the inherent intractability of certain coding problems," IEEE Trans. Inf. Theory, vol. IT-24, no. 3, pp. 384-386, 1978.
4. Q. Cheng and D. Wan, "On the list and bounded distance decodibility of the Reed-Solomon codes (extended abstract) (FOCS)," in Proc. 45th IEEE Symp. Found. Comput. Sci., 2004, pp. 335-341.
5. I. Dumer, D. Micciancio, and M. Sudan, "Hardness of approximating the minimum distance of a linear code," IEEE Trans. Inf. Theory, vol. 49, no. 1, pp. 22-37, 2003.
6. S. Goldwasser and J. Kilian, "Primality testing based on elliptic curves," J. ACM, vol. 46, no. 4, pp. 450-472, 1999.
7. V. Guruswami and A. Vardy, "Maximum-likelihood decoding of Reed-Solomon codes is NP-hard," IEEE Trans. Inf. Theory, vol. 51, no. 7, pp. 2249-2256, 2005.
8. V. Guruswami and M. Sudan, "Improved decoding of reed-solomon and algebraic-geometry codes," IEEE Trans. Inf. Theory, vol. 45, no. 6, pp. 1757-1767, 1999.
9. D. R. H. Brown, "The differences between consecutive primes," J. London Math. Soc., vol. 2, no. 18, pp. 7-13, 1978.
10. M.-D. Huang and D. Ierardi, "Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve," J. Symb. Comput., vol. 18, pp. 519-539, 1994.
11. H. W. Lenstra, "Factoring integers with elliptic curves," Ann. Math., vol. 126, pp. 649-673, 1987.
12. A. Lobstein, "The hardness of solving subset sum with preprocessing," IEEE Trans. Inf. Theory, vol. 36, no. 4, pp. 943-946, 1990.
13. R. Pellikaan, B-Z. Shen, and G. J. M. van Wee, "Which linear codes are algebraic-geometric," IEEE Trans. Inf. Theory, vol. 37, no. 3, pp. 583-602, 1991.
14. J. H. Silverman, The arithmetic of elliptic curves. New York: Springer-Verlag, 1986.
15. A. Vardy, "The intractability of computing the minimum distance of a code," IEEE Trans. Inf. Theory, vol. 43, no. 6, pp. 1757-1766, 1997.