Designs, Codes and Cryptography

, Volume 68, Issue 1–3, pp 141–154 | Cite as

Abelian and non-abelian Paley type group schemes

  • Yu Qing Chen
  • Tao Feng


In this paper, we present a construction of abelian Paley type group schemes which are inequivalent to Paley group schemes. We then determine the equivalence amongst their configurations, the Hadamard designs or the Paley type strongly regular graphs obtained from these group schemes, up to isomorphism. We also give constructions of several families of non-abelian Paley type group schemes using strong multiplier groups of the abelian Paley type group schemes, and present the first family of p-groups of non-square order and of non-prime exponent that contain Paley type group schemes for all odd primes p.


Paley group scheme Paley type group scheme Paley type partial difference set Skew Hadamard difference set 

Mathematics Subject Classification (2000)

05B10 05C25 05E18 05E30 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsWright State UniversityDaytonUSA
  2. 2.Department of MathematicsZhejiang UniversityHangzhouPeople’s Republic of China

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