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A search for affine difference sets of even order

โœ Scribed by Troy D. VanAken

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
407 KB
Volume
62
Category
Article
ISSN
0378-3758

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โœฆ Synopsis

The Prime Power Conjecture asserts that the order of an affine difference set is an integral power of a prime number. K.T. Arasu and D. Jungnickel have shown that if the order of an affine difference set is even, then the order is either two or four or is divisible by eight. This paper extends this direction of research by studying cyclic affine difference sets whose orders are congruent to eight modulo sixteen. In particular, we give several numerical constraints that support the Prime Power Conjecture in this case. We conclude with a computer search for cyclic affine difference sets of order eight modulo sixteen that satisfy these new conditions.

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