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A technique for constructing divisible difference sets

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Abstract

An (m, n, k, λ1,λ2) divisible difference set in a groupG of ordermn relative to a subgroupN of ordern is ak-subsetD ofG such that the list {xy−1:x, y ε D} contains exactly λ1 copies of each nonidentity element ofN and exactly λ2 copies of each element ofG N. It is called semi-regular ifk > λ1 and k2=mnλ2. We develop a method for constructing a divisible difference set as a product of a difference set and a relative difference set or a difference set and a subset ofG which we call a relative divisible difference set. The method results in several parametrically new families of semi-regular divisible difference sets.

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Authors and Affiliations

  1. Central Michigan University, 48859, Mount Pleasant, Michigan, USA

    Yury J. Ionin

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  1. Yury J. Ionin
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Ionin, Y.J. A technique for constructing divisible difference sets. J Geom 67, 164–172 (2000). https://doi.org/10.1007/BF01220307

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  • DOI: https://doi.org/10.1007/BF01220307

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