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Designs, Codes and Cryptography

, Volume 41, Issue 2, pp 195–198 | Cite as

New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices

  • Carl Bracken
  • Gary McGuire
  • Harold Ward
Article

Abstract

Using Hadamard matrices and mutually orthogonal Latin squares, we construct two new quasi-symmetric designs, with parameters 2 − (66,30,29) and 2 − (78,36,30). These are the first examples of quasi-symmetric designs with these parameters. The parameters belong to the families 2 − (2u 2 − u,u 2 − u,u 2 − u − 1) and 2 − (2u 2 + u,u 2,u 2 − u), which are related to Hadamard parameters. The designs correspond to new codes meeting the Grey–Rankin bound.

Keywords

Binary code Grey–Rankin bound Hadamard matrix Mutually orthogonal Latin squares Quasi-symmetric 

AMS Classifications

05B05 05B20 94B65 

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References

  1. 1.
    Bracken C (2004) Designs, codes, spin models and the Walsh transform. PhD Thesis, National University of Ireland, MaynoothGoogle Scholar
  2. 2.
    Dulmage AL, Johnson D, Mendelsohn NS (1960) Orthomorphisms of groups and orthogonal Latin squares. Can J Math 13:356–372MathSciNetGoogle Scholar
  3. 3.
    McGuire G (1997) Quasi-symmetric designs and codes meeting the Grey-Rankin bound. J Combin Theory Ser A 78(2):280–291MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Shrikhande MS (1996) Quasi-symmetric designs. In: Colbourn CJ, Dinitz JH (eds) The CRC handbook of combinatorial designs. CRC Press, Boca Raton, pp 430–434Google Scholar
  5. 5.
    Tonchev VD (1996) Codes. In: Colbourn CJ, Dinitz JH (eds) The CRC handbook of combinatorial designs. CRC Press, Boca Raton, pp 517–543Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mathematics, Maynooth CoNational University of IrelandKildareIreland
  2. 2.Department of MathematicsUniversity of VirginiaCSharlottesvilleUSA

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