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Some Recent Developments in Difference Sets

Davis, James A.; Jedwab, Jonathan


Keyword(s): difference sets; divisible difference sets; recursive

Abstract: There are five known parameter families for (v, k, l, n)-difference sets satisfying gcd(v, n)>1: the Hadamard, McFarland, Spence, Davis-Jedwab, and Chen families. The authors recently gave a recursive unifying construction for difference sets from the first four families which relies on relative difference sets. We give an overview of this construction and show that, by modifying it to use divisible difference sets in place of relative difference sets, the recent difference set discoveries of Chen can be brought within the unifying framework. We also demonstrate the recursive use of an auxiliary construction for divisible difference sets by means of an extended example.

20 Pages

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