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On Lander’s conjecture for difference sets whose order is a power of 2 or 3

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Abstract

Let p be a prime and let b be a positive integer. If a (v, k, λ, n) difference set D of order n = p b exists in an abelian group with cyclic Sylow p-subgroup S, then \({p\in\{2,3\}}\) and |S| = p. Furthermore, either p = 2 and v ≡ λ ≡ 2 (mod 4) or the parameters of D belong to one of four families explicitly determined in our main theorem.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Kent Ridge, Singapore, 119260, Republic of Singapore

    Ka Hin Leung & Siu Lun Ma

  2. Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore

    Bernhard Schmidt

Authors
  1. Ka Hin Leung
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  2. Siu Lun Ma
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  3. Bernhard Schmidt
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Correspondence to Bernhard Schmidt.

Additional information

Communicated by Alexander Pott.

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Leung, K.H., Ma, S.L. & Schmidt, B. On Lander’s conjecture for difference sets whose order is a power of 2 or 3. Des. Codes Cryptogr. 56, 79–84 (2010). https://doi.org/10.1007/s10623-009-9344-5

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  • DOI: https://doi.org/10.1007/s10623-009-9344-5

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