Nonexistence of certain supplementary difference sets

Publisher： Cambridge University Press

E-ISSN： 1755-1633|13|3|343-348

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.13, Iss.3, 1975-12, pp. : 343-348

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Abstract

This paper finds restrictions on the parameters of supplementary difference sets in any group G with a subgroup of index 2, which therefore includes all cyclic groups of even orders. As a corollary to the main theorem, we have that if S1, …, Sr are r − {2v, k1, …, kr; 2λ} supplementary difference sets in such a group, then not all of v, k1, …, kr, λ are odd; also is the sum of r squares.

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