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Anticodes for the Grassman and bilinear forms graphs

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Abstract

In [2], L. Chihara proved that many infinite families of classical distance-regular graphs have no nontrivial perfect codes, including the Grassman graphs and the bilinear forms graphs. Here, we present a new proof of her result for these two families using Delsarte's anticode condition[3]. The technique is an extension of an approach taken by C. Roos [6] in the study of perfect codes in the Johnson graphs.

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References

  1. A. E. Brouwer, A. M. Cohen, and A. Neumaier,Distance-Regular Graphs, Springer-Verlag, Berlin (1989).

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  2. L. Chihara, On the zeros of the Askey-Wilson polynomials with applications to coding theory,SIAM J. Math. Anal., Vol. 18 (1987) pp. 191–207.

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  3. P. Delsarte, An algebraic approach to the association schemes of coding theory,Philips Res. Reports Suppl., Vol. 10 (1973).

  4. D. E. Knuth, Subspaces, subsets, and partitions.J. Combin. Th. (A), Vol. 10 (1971) pp. 178–180.

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  5. D. A. Leonard, Orthogonal polynomials, duality, and association schemes,SIAM J. Math. Anal., Vol. 13 (1982) pp. 656–663.

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  6. C. Roos, A note on the existence of perfect constant weight codes.Discrete Math., Vol. 47 (1983) pp. 121–123.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics & Statistics, University of Winnipeg, Winnipeg, Manitoba

    W. J. Martin

  2. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario

    X. J. Zhu

Authors
  1. W. J. Martin
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  2. X. J. Zhu
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Martin, W.J., Zhu, X.J. Anticodes for the Grassman and bilinear forms graphs. Des Codes Crypt 6, 73–79 (1995). https://doi.org/10.1007/BF01390772

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  • DOI: https://doi.org/10.1007/BF01390772

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