Design theory
Designs and their codes
Combinatorial theory (2nd ed.)
Combinatorial theory (2nd ed.)
Multiplicative Difference Sets via Additive Characters
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
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Dillon and Dobbertin proved that if L := GF(2 m ), gcd(k, m) = 1, d := 4 k 驴 2 k + 1 and Δ k (x) := (x + 1) d + x d + 1, then B k := L\Δ k (L) is a difference set in the cyclic multiplicative group L 脳 of L. Used in the proof were the auxiliary functions $$c_k^{\gamma}(x) := b_k(\gamma x^{2^k+1})$$ , where 驴 is in L 脳 and b k is the characteristic function of B k on L. When m is odd $$c_k^{\gamma}$$ is itself the characteristic function of a cyclic difference set which is equivalent to B k . In this paper we point out that when m is even and 驴 is not a cube in L then $$c_k^{\gamma}$$ is the characteristic function of a difference set in the elementary abelian additive group of L; i.e. $$c_k^{\gamma}$$ is a bent function.