Network generalized hamming weight

IEEE Transactions on Information Theory

Volumn 57, Issue 2, 2011, Pages 1136-1143

  Ngai, Chi Kin ^a   Yeung, Raymond W ^a   Zhang, Zhixue ^a,b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

Algebraic coding; cryptography; generalized Hamming weight; MDS code; multicast; network coding; secret sharing; wiretap channel

Indexed keywords

ALGEBRAIC CODING; GENERALIZED HAMMING WEIGHT; MDS CODE; MULTICASTS; NETWORK CODING; SECRET SHARING; WIRETAP CHANNEL;

ALGEBRA; COMPUTER PROGRAMMING; CRYPTOGRAPHY; INFORMATION THEORY; LINEAR NETWORKS; MULTICASTING;

ENCODING (SYMBOLS);

EID: 79251515754     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2095233     Document Type: Article

References (20)

1. V. K. Wei, "Generalized Hamming weight for linear codes," IEEE Trans. Inf. Theory, vol. 37, no. 6, pp. 1412-1418, Sep. 1991.
2. L. H. Ozaro and A. D.Wyner, "Wire-tap-channel II," AT& T Bell Labs Tech. J., vol. 63, pp. 2135-2157, 1984.
3. G. R. Blakley, "Safeguarding cryptographic keys," in Proc. National Computer Conf., 1979, vol. 48, pp. 313-317.
4. A. Shamir, "How to share a secret," in Commun. ACM, 1979, vol. 22, pp. 612-613.
5. N. Cai and R. W. Yeung, "Secure network coding," in Proc. 2002 IEEE Int. Symp. Information Theory, Lausanne, Switzerland, Jun. 2002.
6. S. E. Rouayheb and E. Soljanin, "On wiretap networks II," in Proc. 2007 IEEE Int. Symp. Information Theory, Jun. 2007.
7. S. Jaggi et al., "Polynomial time algorithms for multicast network code construction," IEEE Trans. Inf. Theory, vol. 51, no. 6, pp. 1973-1982, Jun. 2005.
8. R. W. Yeung, Information Theory and Network Coding. New York: Springer, 2008.
9. C. K. Ngai, "Network coding for security and error correction," Ph.D. dissertation, CUHK, Hong Kong, 2008.
10. S. E. Rouayheb, E. Soljanin, and A. Springton, "Secure network coding for wiretap networks of type II," IEEE Trans. Inf. Theory., submitted for publication.
11. B. Bollobas, Graph Theory, An Introductory Course. New York: Springer-Verlag, 1979.
12. L. K. Ford Jr. and D. K. Fulkerson, Flows in Networks. Princeton, NJ: Princeton University Press, 1962.
13. R. C. Singleton, "Maximum distance q-nary codes," IEEE Trans. Inf. Theory, vol. IT-10, no. 2, pp. 116-118, Apr. 1964.
14. R. W. Yeung and N. Cai, "Network error correction, Part I: Basic concepts and upper bounds," Commun. Info. and Syst., vol. 6, pp. 19-36, 2006.
15. N. Cai and R. W. Yeung, "Network error correction, Part II: Lower bounds," Commun. Info. and Syst., vol. 6, pp. 37-54, 2006.
16. M. Langberg, A. Sprintson, and J. Bruck, "Network coding: A computational perspective," IEEE Trans. Inf. Theory, vol. 55, no. 1, pp. 147-157, Jan. 2009.
17. N. Cai and R. W. Yeung, "Secure network coding in wiretap network," IEEE Trans. Inf. Theory., submitted for publication.
18. S. Yang and R. W. Yeung, "Refined coding bounds for network error correction," in Proc. 2007 IEEE Information Theory Workshop, Bergen, Norway, Jul. 2007.
19. S. Yang and R. W. Yeung, "Characterizations of network error correction/ detection and erausre correction," in Proc. 3rd Workshop on Network Coding, Theory, and Applications (NetCod 2007), San Diego, CA, Jan. 2007.
20. S. Yang, R. W. Yeung, and Z. Zhang, "Weight properties of network codes," Eur. Trans. Telecomm., vol. 19, pp. 371-383, 2008.