Dimension/Length Profiles and Trellis Complexity of Linear Block Codes

IEEE Transactions on Information Theory

Volumn 40, Issue 6, 1994, Pages 1741-1752

  Forney, G David ^a  

^a MOTOROLA INC   (United States)

Author keywords

Dimension length profiles; generalized; Hamming weights; linear codes; state complexity; support weights; trellis diagrams

Indexed keywords

HIERARCHICAL SYSTEMS; SIGNAL ENCODING; TRELLIS CODES;

DIMENSION/LENGTH PROFILES; GENERALIZED HAMMING WEIGHT HIERARCHY; MAXIMUM DISTANCE SEPARABLE (MDS) CODE; STATE COMPLEXITY; TRELLIS DIAGRAMS;

BLOCK CODES;

EID: 0028547151     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.340452     Document Type: Article

References (22)

1. V. K. Wei, “Generalized Hamming weights for linear codes,'’ IEEE Trans. Inform. Theory, vol. 37, pp. 1412-1418, Sept. 1991.
2. T. Helleseth, T. Klϕve, and J. Mykkelveit, “The weight distribution of irreducible cyclic codes with block lengths n1((ql - 1)/N)n,” Discr. Math., vol. 18, pp. 179-211, 1977.
3. T.Klϕve, “Support weight distribution of linear codes,” Discr. Math., vol. 107, pp. 311-316, 1992.
4. J. Simonis, “The effective length of subcodes,” preprint.
5. G. D. Forney, Jr., “Coset codes—Part II: Binary lattices and related codes,” IEEE Trans. Inform. Theory, vol. 34, pp. 1152-1187, Sept. 1988.
6. G. D. Forney, Jr. and M. D. Trott, “The dynamics of group codes: State spaces, trellis diagrams and canonical encoders,” IEEE Trans. Inform. Theory, vol. 39, pp. 1491-1513, Sept. 1993.
7. T. Kasami, T. Takata, T. Fujkiwara, and S. Lin, “On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 242-245, Jan. 1993.
8. A. Vardy and Y. Be’ery, “Maximum-likelihood soft-decision decoding of BCH codes,” IEEE Trans. Inform. Theory, vol. 40, pp. 546-554, March 1994.
9. Ytrehus, “On the trellis complexity of linear block codes,” IEEE Trans. Inform. Theory, to appear.
10. A. E. Brouwer and T. Verhoeff, “An updated table of minimum-distance bounds for binary linear codes,” IEEE Trans. Inform. Theory, vol. 39, 662-677, Mar. 1993.
11. D. Muder, “Minimal trellises for block codes,” IEEE Trans. Inform. Theory, vol. 34, pp. 1049-1053, Sept. 1988.
12. J. K. Wolf, “Efficient maximum likelihood decoding of linear block codes,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 76-80, Jan. 1978.
13. T. Helleseth, T. Klϕve, and ϕ. Ytrehus, “Generalized Hamming weights of linear codes,” IEEE Trans. Inform. Theory, vol. 38, pp. 1133-1140, May 1992.
14. T. Klϕve, “Minimum support weights of binary codes,” IEEE Trans. Inform. Theory, vol. 39, pp. 648-654, Jan. 1993.
15. J. H. Conway and N. J. A. Sloane, “Lexicographic codes: Error-correcting codes from game theory,” IEEE Trans. Inform. Theory, vol. IT-32, pp. 337-348, May 1986.
16. V. K. Wei and K. Yang, “On the generalized Hamming weights of product codes,” IEEE Trans. Inform. Inform. Theory, vol. 39, pp. 1709-1713, Sept. 1993.
17. S. Encheva and T. Klϕve, “Codes satisfying the chain condition,” IEEE Trans. Inform. Theory, vol. 40, pp. 175-180, Jan. 1994.
18. T. Helleseth and P. V. Kumar, “The weight hierarchy of the Kasami codes,” Discr. Math., to appear.
19. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane, and P. Sole, “The Z4-linearity of Kerdock, Preparata, Goethals, and related codes,” IEEE Trans. Inform. Theory, vol. 40, pp. 301-319, Mar. 1994.
20. G. D. Forney, Jr., N. J. A. Sloane, and M. D. Trott, “The Nordstrom-Robinson code is the binary image of the octacode,” in Coding and Quantization: DIMACS/IEEE Workshop (Oct. 19-21, 1992), R. Calderbank et al., eds., Providence, RI: Am. Math. Soc., 1993, pp. 19-26.
21. G. D. Forney, Jr., “Density/length profiles and trellis complexity of lattices,” IEEE Trans. Inform. Theory, vol. 40, pp. 1753-1773, Nov. 1994.
22. V. K. Wei, “A survey of results on generalized Hamming weights for linear codes,” in Proc. 1993 IEEE Inform. Theory Workshop, (Susono, Japan), June 1993, pp. 45-46.