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PBIBDs from weakly divisible nearrings and related codes

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Abstract

In [5] the authors are able to give a method for the construction of a family of partially balanced incomplete block designs from a special class of wd-nearrings (wd-designs). In this paper the wd-design incidence matrix and the connected row and column codes are studied. The parameters of two special classes of wd-designs and those of the related row and column codes are calculated.

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References

  1. Assmus Jr., E.F. and Key, J.D., Designs and their codes, Cambridge Tractas in Mathhematics, Cambridge University Press, NY 1992.

    MATH  Google Scholar 

  2. Bannai, E., Introduction to association schemes, Methods of Discrete Mathematics, (Braunschweig,1999), 1–70.

  3. Benini, A. and Morini, F., Weakly divisible nearrings on the group of integers (mod pn), Riv. Mat. Univ. Parma, (6) 1 (1998), 1–11.

    MathSciNet  MATH  Google Scholar 

  4. Benini, A. and Morini, F., On the construction of a class of weakly divisible nearrings, Riv. Mat. Univ. Parma, (6) 1 (1998), 103–111.

    MathSciNet  MATH  Google Scholar 

  5. Benini, A. and Morini, F., Partially Balanced Incomplete Block Designs from Weakly Divisible Nearrings, Sem. Mat. Brescia, Quad. 17 (2004), preprint.

  6. Benini, A. and Pellegrini, S., Weakly Divisible Nearrings, Discrete Math. 208/209 (1999), 49–59.

    Article  MathSciNet  Google Scholar 

  7. Beth, T., Jungnickel, D. and Lenz, H., Design Theory, Encyclopedia of Mathematics and its Applications, 69. Cambridge University Press, Cambridge 1999.

    Google Scholar 

  8. Clay, J.R., Nearrings: Geneses and Applications, Oxford Science Publications, Oxford University Press, NY 1992.

    MATH  Google Scholar 

  9. Davis, P.J., Circulant matrices, 2nd. ed., Chelsea Publishing, New York, NY 1994.

    MATH  Google Scholar 

  10. Hall, M., Designs with transitive authomorphism group, Proc. of Symposia in Pure Math. AMS, T. L. Motzkin, ed., (1971), 109–113.

  11. Lancaster, P. and Timenetsky, M., The theory of matrices, 2nd. ed. Academic Press, 1985.

  12. McWilliams, F.J. and Sloane, N.J.A., The theory of Error-correcting Codes, North-Holland Amsterdam 1977.

  13. Penfold Street, A. and Street, D.J., Combinatorics of Experimental Design Oxford University Press, New York, 1987.

    MATH  Google Scholar 

  14. Pilz, G., Near-rings, 2nd. ed., North Holland Math. Studies 23, Amsterdam, 1983.

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  1. Dipartimento di Matematica, Facoltá di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, I-25133, Brescia, Italy

    Anna Benini

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  1. Anna Benini
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Correspondence to Anna Benini.

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Work carried out on behalf of Italian M.I.U.R.

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Benini, A. PBIBDs from weakly divisible nearrings and related codes. Results. Math. 47, 6–16 (2005). https://doi.org/10.1007/BF03323008

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