There are five known parameter families for (v, k, λ, 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.
Copyright © 1999 Chapman & Hall/CRC Press. This chapter first appeared in Combinatorial Designs and Their Applications.
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Davis, James A., and Jonathan Jedwab. "Some Recent Developments in Difference Sets." In Combinatorial Designs and Their Applications, edited by Kathleen Quinn, Bridget Webb, Chris Rowley, and F. C. Holroyd, 83-102. Chapman & Hall/CRC Research Notes in Mathematics Series. New York: Chapman &Hall/CRC Press, 1999.