Approximating the maximum weight of linear codes is APX-complete

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E83-A, Issue 4, 2000, Pages 606-613

  Itoh, Toshiya ^a  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Approximation algorithms; APX complete; Linear codes; Maximum weight

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CODES (SYMBOLS); DECODING; ERROR CORRECTION; MATRIX ALGEBRA;

LINEAR CODES;

COMPUTATIONAL COMPLEXITY;

EID: 0033702071     PISSN: 09168508     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. G. Ausiello, P. Crescenzi, and M. Protasi, "Approximate solution of NP optimization problems," Theor. Comput. Sci., vol.150, pp.1-55, 1995.
2. N. Alon and J.H. Spencer, The Probabilistic Method, John Wiley & Sons, 1992.
3. E.R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, 1968.
4. E.R. Berlekamp, R.J. McEliece, and C.A. van Tilborg, "On the inherent intractability of certain coding problems," IEEE Trans, on Inform. Theory, vol.24, pp.384-386, 1978.
5. I. Dinur, D. Micciancio, and M. Sudan, "Hardness of approximating the minimum distance of a linear code," Electronic Colloquium on Computational Complexity, Report no.29, 1999.
6. J. Håstad, "Some optimal inapproximability results," Proc. 29th Annual ACM Symposium on Theory of Computing, pp.1-10, 1997.
7. D.S. Johnson, "A catalog for complexity classes," Handbook of Theoretical Computer Science, vol.A, Elsevier Science, 1990.
8. M. Karpovsky, "Weight distribution of translates, covering radius, and perfect codes," IEEE Trans. Inform. Theory, vol.27, pp.462-472, 1981.
9. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, 9th ed., North-Holland, 1996.
10. S.C. Ntafos and S.L. Hakimi, "On the complexity of some coding problems," IEEE Trans. Inf. Theory, vol.27, pp.794-796, 1981.
11. E. Petrank, "The hardness of approximation: Gap location," Technical Report #754, Technion - Israel Institute of Technology, 1992.
12. C.H. Papadimitriou and M. Yannakakis, "Optimization, approximation, and complexity classes," J. Comput. System Sci., vol.43, no.3, pp.425-440, 1991.
13. J. Stern, "Approximating the number of error locations within a constant ratio is NP-complete," Proc. Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes, Lecture Notes in Computer Science 673, pp.325-331, 1993.
14. A. Vardy, "The intractability of computing the minimum distance of a code," IEEE Trans. Inf. Theory, vol.43, pp.1757-1766, 1997.