Covering Radius, Codimension, and Dual-Distance Width

IEEE Transactions on Information Theory

Volumn 39, Issue 4, 1993, Pages 1195-1203

  Stokes, Philip ^b  

^a CNRS   (France)

^b NONE   (United Kingdom)

Author keywords

Covering radius; dual distance; group algebras; Krawtchouk polynomials

Indexed keywords

ALGEBRA; CODES (SYMBOLS); GRAPHIC METHODS; MATHEMATICAL MODELS; POLYNOMIALS; THEOREM PROVING;

COVERING RADIUS; DUAL DISTANCE; GROUP ALGEBRAS; KRAWTCHOUK POLYNOMIALS;

INFORMATION THEORY;

EID: 0027629032     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.243438     Document Type: Article

References (22)

1. T. Helleseth, T. Klove, and J. Mykkeltveit, “On the covering radius of binary codes,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 627–628, 1978.
2. P. Sole and K. G. Mehrotra, “Generalization of the Norse bounds to codes of higher strength,” IEEE Trans. Inform. Theory, vol. 37, pp. 190–192, Jan. 1991.
3. P. Sole, “Asymptotic bounds on the covering radius of binary codes,” IEEE Trans. Inform. Theory, vol. 36, pp. 1470–1472, Nov. 1990.
4. A. A. Tietaviiinen, “An upper bound on the covering radius as a function of the dual distance,” IEEE Trans. Inform. Theory, vol. 36, pp. 1472–1474, Nov. 1990.
5. A. A. Tietaviiinen, “Covering radius and dual distance,” Designs, Codes and Cryptography, vol. 1, pp. 31–46, 1991.
6. C. Delorme and P. Sole, “Diameter, covering index, covering radius and eigenvalues,” European J. Combinat., vol. 12, pp. 95–108, 1991.
7. P. Delsarte, “Pairs of vectors in the space of an association scheme,” Philips Res. Rep. 27, pp. 373–411, 1977.
8. P. Camion, B. Courteau, and P. Delsarte, “On γ-partition designs in Hamming spaces,” vol. AAECC 2, pp. 147–162, 1992.
9. P. Solé and P. Stokes, I3S Research Report 91–9.
10. P. Stokes, Ph.D. thesis, Univ. of London, Queen Mary and Westfield College, 1992.
11. J. H. van Lint, Introduction to Coding Theory. New York: SpringerVerlag, Verlag, 1982.
12. J. H. van Lint and T. A. Springer, “Generalized Reed-Solomon codes from-algebraic geometry,” IEEE Trans. Inform. Theory, vo l. IT-33, pp. 305–309, May 1987.
13. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam: North-Holland, 1977.
14. E. Bannai and T. Ito, Algebraic Combinatorics I—Association Schemes. CA: Benjamin-Cummins, 1984.
15. T. Kasami, T. Fujiwara, and S. Lin, “An approximation to the weight distribution of binary linear codes,” IEEE Trans. Inform. Theory, vol. IT-31, pp. 769–780, Nov. 1985.
16. M. J. Aaltonen, “Linear programming bounds for tree codes,” IEEE Trans. Inform. Theory, vo l. IT-25, pp. 85–90, 1979.
17. G. Lachaud and J. Stem, “Polynomial-time construction of codes I: linear codes with almost equal weights,” AAECC, to appear.
18. C. J. Moreno and O. Moreno, “Exponential Sums and Goppa Codes IV,” preprint.
19. R. Pellikaan, B. Z. Shen, and G. J. M. van Wee, “Which linear codes are algebraic geometric?,” IEEE Trans. Inform. Theory, vol. 37, pt. I, pp. 583–602, May 1991.
20. A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance Regular Graphs. New York: Springer-Verlag, 1989.
21. D. M. Cvetkovie, M. Doob, and H. Sachs, Spectra of Graphs—Theory and Application. New York: Academic Press, 1979.
22. N. Biggs, Algebraic Graph Theory. Cambridge: Cambridge Univ. Press, 1974.