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An Infinite Family of 3-Designs from Preparata Codes overZ4

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Abstract

We show that the support of minimum Lee weight codewords having Hamming weight 5 in the Preparata code over Z4 form a 3-(2m,5,10) design for any odd integer m ≥ 3.

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References

  1. W. O. Alltop, An infinite class of 4-designs, J. Combin. Theory., Vol. 6 (1969) pp. 320–322.

    Google Scholar 

  2. E. F. Assmus, Jr. and H. F. Mattson, Jr., New 5-designs, J. Combin. Theory., Vol. 6 (1969) pp. 122–151.

    Google Scholar 

  3. A. H. Baartmans, I. Bluskov, and V. Tonchev, The Preparata codes and a class of 4-designs, J. Combin. Designs, Vol. 2, No.3 (1994) pp. 167–170.

    Google Scholar 

  4. J. Bierbrauer, A new family of 4-designs, Graphs and Combinatorics, Vol. 11 (1995) pp. 209–211.

    Google Scholar 

  5. A. 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 (1994) pp. 301–319.

    Article  Google Scholar 

  6. M. Harada, New 5-designs constructed from the lifted Golay code over Z4, preprint, presented at the Recent Results Session of 1997 IEEE International Symposium on Information Theory, Ulm, Germany, June 29-July 4, 1997.

  7. T. Helleseth and P. V. Kumar, The algebraic decoding of the Z4-linear Goethals code, IEEE Trans. Inform. Theory, Vol. 41 (1995) pp. 2040–2048.

    Article  Google Scholar 

  8. P. V. Kumar, T. Helleseth, and A. R. Calderbank, An upper bound for Weil exponential sums over Galois rings and its applications, IEEE Trans. Inform. Theory, Vol. 41 (1995) pp. 456–468.

    Google Scholar 

  9. R. Lidl and H. Niederreiter, Finite Fields, Vol. 20 of Encyclopedia of Mathematics and Its Applications. Reading, MA: Addison-Wesley (1983).

    Google Scholar 

  10. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland (1977).

  11. V. Tonchev, A class of Steiner 4-wise balanced designs derived from Preparata codes, J. Combin. Designs, Vol. 4, No.3 (1996) pp. 203–204.

    Article  Google Scholar 

  12. K. Yang and T. Helleseth, On the weight hierarchy of the Preparata code over Z4, IEEE Trans. Inform. Theory, Vol. 43 (1997) pp. 1832–1842.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, Hoyteknologisenteret, N-5020, Bergen, Norway

    Tor Helleseth

  2. Communication Sciences Institute, EE-Systems, University of Southern California, Los Angeles, CA, 90089-2565, USA

    P. Vijay Kumar

  3. Department of Electronic Communication Engineering, Hanyang University, Seoul, 133-791, Korea

    Kyeongcheol Yang

Authors
  1. Tor Helleseth
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  2. P. Vijay Kumar
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  3. Kyeongcheol Yang
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Helleseth, T., Kumar, P.V. & Yang, K. An Infinite Family of 3-Designs from Preparata Codes overZ4. Designs, Codes and Cryptography 15, 175–181 (1998). https://doi.org/10.1023/A:1008363617109

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