Error-correcting codes in projective spaces via rank-metric codes and ferrers diagrams

IEEE Transactions on Information Theory

Volumn 55, Issue 7, 2009, Pages 2909-2919

  Etzion, Tuvi ^a   Silberstein, Natalia ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Constant dimension codes; Constant weight codes; Ferrers diagram; Identifying vector; Network coding; Projective space codes; Puncturing; Rank metric codes; Reduced row echelon form

Indexed keywords

CONSTANT-DIMENSION CODES; CONSTANT-WEIGHT CODES; FERRERS DIAGRAM; IDENTIFYING VECTOR; NETWORK CODING; PROJECTIVE SPACE CODES; PUNCTURING; RANK-METRIC CODES; REDUCED ROW ECHELON FORM;

ARTIFICIAL INTELLIGENCE; BINARY CODES; DECODING; INFORMATION THEORY; SIGNAL ENCODING; TOPOLOGY;

METRIC SYSTEM;

EID: 67650156080     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2021376     Document Type: Article

References (25)

1. R. Ahlswede, H. K. Aydinian, and L. H. Khachatrian, "On perfect codes and related concepts," Des., Codes Cryptogr., vol. 22, pp. 221-237, 2001.
2. R. Koetter and F. R. Kschischang, "Coding for errors and erasures in random network coding," IEEE Trans. Inf. Theory, vol. 54, no. 8, pp. 3579-3591, Aug. 2008.
3. D. Silva, F. R. Kschischang, and R. Koetter, "A rank-metric approach to error control in random network coding," IEEE Trans. Inf. Theory, vol. 54, no. 9, pp. 3951-3967, Sep. 2008.
4. T. Etzion and A. Vardy, "Error-correcting codes in projective space," in Proc. IEEE Int. Symp. Information Theory, Toronto, ON, Canada, Jul. 2008, pp. 871-875.
5. E. M. Gabidulin and M. Bossert, "Codes for network coding," in Proc. IEEE Int. Symp. Information Theory, Toronto, ON, Canada, Jul. 2008, pp. 867-870.
6. M. Gadouleau and Z. Yan, "On the Connection Between Optimal Constant-Rank Codes and Optimal Constant-Dimension Codes," arxiv.org/abs/0803.2262.
7. M. Gadouleau and Z. Yan, "Constant-rank codes," in Proc. IEEE Int. Symp. Information Theory, Toronto, ON, Canada, Jul. 2008, pp. 876-880.
8. A. Kohnert and S. Kurz, "Construction of Large Constant Dimension Codes With a Prescribed Minimum Distance," arxiv.org/abs/0807.3212.
9. F. Manganiello, E. Gorla, and J. Rosenthal, "Spread codes and spread decoding in network coding," in Proc. IEEE Int. Symp. Information Theory, Toronto, ON, Canada, Jul. 2008, pp. 881-885.
10. V. Skachek, "Recursive Code Construction for Random Network," arxiv.org/abs/0806.3650.
11. S. T. Xia and F. W. Fu, "Johnson type bounds on constant dimension codes," Des., Codes, Cryptogr., vol. 50, pp. 163-172, 2009.
12. E. M. Gabidulin, "Theory of codes with maximum rank distance," Probl. Inf. Transm., vol. 21, pp. 1-12, Jul. 1985.
13. R. M. Roth, "Maximum-rank array codes and their application to crisscross error correction," IEEE Trans. Inf. Theory, vol. 37, no. 2, pp. 328-336, Mar. 1991.
14. D. E. Knuth, "Subspaces, subsets. and partitions," J. Combin. Theory, vol. 10, pp. 178-180, 1971.
15. J. H. van Lint and R. M. Wilson, A Course in Combinatorics. Cambridge, U.K.: Cambridge Univ. Press, 1992.
16. G. E. Andrews and K. Eriksson, Integer Partitions. Cambridge, U.K.: Cambridge Univ. Press, 2004.
17. R. P. Stanley, Enumerative Combinatorics. Monterey, CA: Wadsworth, 1986, vol. 1.
18. S. Milne, "Mappings of subspaces into subsets," J. Comb. Theory, ser. A, vol. 33, pp. 36-47, 1982.
19. P. Delsarte, "Bilinear forms over a finite field, with applications to coding theory," J. Comb. Theory, ser. A, vol. 25, pp. 226-241, 1978.
20. J. H. Conway and N. J. A. Sloane, "Lexicographic codes: Error-correcting codes from game theory," IEEE Trans. Inf. Theory vol. IT-32, no. 3, pp. 337-348, May 1986.
21. R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeung, "Network information flow," Des., Codes, Cryptogr., vol. 46, pp. 1204-1216, July 2000.
22. T. Ho, M. Médard, R. Koetter, D. R. Karger, M. Effros, J. Shi, and B. Leong, "A random linear network coding approach to multicast," IEEE Trans. Inf. Theory, vol. 52, no. 10, pp. 4413-4430, Oct. 2006.
23. T. Ho, R. Koetter, M. Médard, D. R. Karger, and M. Effros, "The benefits of coding over routing in a randomized setting," in Proc. IEEE Int. Symp. Information Theory, Yokohoma, Japan, Jun./Jul. 2003, p. 442.
24. N. Cai and R. W. Yeung, "Network error correction, part II: Lower bounds," Commun. Inf. Systist., vol. 6, pp. 37-54, May 2006.
25. R. W. Yeung and N. Cai, "Network error correction, part I: Basic concepts and upper bounds," Commun. Inf. Systist., vol. 6, pp. 19-36, May 2006.