Abstract
A subset S of an additive group G is said to be a sum-free set if S ∩ (S + S) = Ø. A sum-free set S is said to be locally maximal if for every sum-free set T such that S⊑T⊑G, we have S = T.Here we determine some sum-free cyclotomic classes in finite fields and from them, we construct new supplementary difference sets, association schemes and block designs. We also continue our study of locally maximal sum-free sets in groups of small orders and in finite fields.
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