Difference Sets with n = 2pm

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Abstract

Let D be a (v, k, λ) difference set over an abelian group G with even n = k - λ. Assume that t ∈ N satisfies the congruences t = qfii (mod exp(G)) for each prime divisor qi of n/2 and some integer fi. In [4] it was shown that t is a multiplier of D provided that n > λ, (n/2, λ) = 1 and (n/2, v) = 1. In this paper we show that the condition n > λ may be removed. As a corollary we obtain that in the case of n = 2pa when p is a prime, p should be a multiplier of D. This answers an open question mentioned in [2].

Original languageEnglish
Pages (from-to)77-89
Number of pages13
JournalJournal of Algebraic Combinatorics
Volume7
Issue number1
DOIs
StatePublished - 1 Jan 1998
Externally publishedYes

Keywords

  • Abelian group
  • Difference set

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