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Uniqueness of some cyclic projective planes

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Abstract

For n < 41 and for \({{n \in }}\) {121, 125, 128, 169, 256, 1024}, every cyclic projective plane of order n is desarguesian.

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References

  1. Baumert L.D., Gordon D.M.: On the existence of cyclic difference sets with small parameters. In: High Primes and Misdemeanours: Lectures in Honour of the 60th Birthday of Hugh Cowie Williams. Fields Inst. Commun. 41, 61–68 (2004)

    MathSciNet  Google Scholar 

  2. Beth T., Jungnickel D., Lenz H.: Design Theory, 2nd edn. Cambridge University Press (1999).

  3. Bruck R.H.: Quadratic extensions of cyclic planes. Proc. Symp. Appl. Math. 10, 15–44 (1960)

    MathSciNet  Google Scholar 

  4. Gordon D.M.: The prime power conjecture is true for n < 2,000,000. J. Comb. 1, 101–107 (1994)

    Google Scholar 

  5. Gordon B., Mills W.H., Welch L.R.: Some new difference sets. Can. J. Math. 14, 614–625 (1962)

    MATH  MathSciNet  Google Scholar 

  6. Hall M.: Cyclic projective planes. Duke Math. J. 14, 1079–1090 (1947)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hall M.: A survey of difference sets. Proc. Am. Math. Soc. 7, 975–986 (1957)

    Article  MATH  Google Scholar 

  8. Jungnickel D.: The isomorphism problem for Abelian projective planes. Appl. Algebra Eng. Commun. Comput. 19, 195–200 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  9. McFarland R.L., Rice B.F.: Translates and multipliers of abelian difference sets. Proc. Am. Math. Soc. 68, 375–379 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  10. Singer J.: A theorem in finite projective geometry and some applications to number theory. Trans. Am. Math. Soc. 43, 377–385 (1938)

    Article  MATH  Google Scholar 

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Correspondence to Bernhard Schmidt.

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Communicated by D.Jungnickel.

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Huang, Y., Schmidt, B. Uniqueness of some cyclic projective planes. Des. Codes Cryptogr. 50, 253–266 (2009). https://doi.org/10.1007/s10623-008-9229-z

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  • DOI: https://doi.org/10.1007/s10623-008-9229-z

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