Binary codes derived from the hoffman-singleton and higman-sims graphs

IEEE Transactions on Information Theory

Volumn 43, Issue 3, 1997, Pages 1021-1025

  Tonchev, Vladimir D ^a  

^a MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

Author keywords

Majority decoding; Optimal linear code; Strongly regular graph

Indexed keywords

DECODING; FORMAL LOGIC; GRAPH THEORY; MATRIX ALGEBRA; OPTIMIZATION;

LOGIC DECODING;

BINARY CODES;

EID: 0031143280     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.568714     Document Type: Article

References (23)

1. E. F. Assmus, Jr. and J. D. Key, Designs and their Codes. Cambridge, U.K.: Cambridge Univ. Press, 1992.
2. T. Beth, D. Jungnickel, and H. Lenz, Design Theory. Cambridge, U.K.: Cambridge Univ. Press, 1986.
3. R. E. Blahut, Algebraic Methods for Signal Processing and Communications Coding. New York: Springer-Verlag, 1992.
4. A. E. Brouwer and C.A. van Eijl, "On the p-rank of the adjacency matrices of strongly regular graphs," J. Alg. Combin., vol. 1, pp. 329-346, 1992.
5. A. E. Brouwer and T. Verhoeff, "An updated table of minimum-distance bounds for binary linear codes," IEEE Trans. Inform. Theory, vol. 39, pp. 662-677, 1993.
6. P. J. Cameron and J. H. van Lint, Graphs, Codes and Designs. Cambridge, U.K.: Cambridge Univ. Press, 1980.
7. A. R. Calderbank and D. B. Wales, "A global code invariant under the Higman-Sims group," J. Algebra, vol. 75, pp. 233-260, 1982.
8. J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups. Oxford, U.K.: Clarendon, 1985.
9. 3," J. Comb., Theory, vol. A 62, pp. 225-233, 1993.
10. M. Hall, Jr., Combinatorial Theory, 2nd ed. New York: Wiley, 1986.
11. G. Higman, "On the simple group of D. G. Higman and C. C. Sims," Illinois J. Math., vol. 13, pp. 74-80, 1969.
12. A. J. Huffman and R. R. Singleton, "On Moore graphs with diameter 2 and 3," IBM J. Res. Develop., vol. 4, pp. 497-504, 1960.
13. D. G. Higman and C. C. Sims, "A simple group of order 44,352,000," Math. Z., vol. 105, pp. 110-113, 1968.
14. X. Hubaut, "Strongly regular graphs," Discr. Math., vol. 13, pp. 357-381, 1975.
15. W. M. Kantor and R. A. Liebler, "The rank 3 permutation representations of the finite classical groups," Trans. Amer. Math. Soc., vol. 271, pp. 1-71, 1982.
16. M. W. Liebeck, "The affine permutation groups of rank three," Proc. London. Math Soc. (3), vol. 54, pp. 477-516, 1987.
17. M. W. Liebeck and J. Saxl, "The finite primitive permutation groups of rank three," Bull. London Math. Soc., vol. 18, pp. 165-172, 1986.
18. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
19. C. Parker and V. D. Tonchev, "Linear codes and doubly-transitive symmetric designs," Lin. Alg. and its Appl., vol. 226-228, pp. 237-246, 1995.
20. V. Pless, Introduction to the Theory of Error-Correcting Codes. New York: Wiley, 1989.
21. R. Peelers, "Uniqueness of strongly regular graphs with minimal p-rank," Lin. Alg. and its Appl.. vol. 226-228, pp. 9-31, 1995.
22. L. D. Rudolph, "A class of majority-logic decodable codes," IEEE Trans. Inform. Theory, vol. IT-13, pp. 305-307, 1967.
23. V. D. Tonchev, Combinatorial Configurations. New York: Longman, Wiley, 1988.