Abstract
We determine the functions on GF (2) n which satisfy the propagation criterion of degree n −2, PC ( n −2). We study subsequently the propagation criterion of degree ℓ and order k and its extended version EPC . We determine those Boolean functions on GF (2) n which satisfy PC (ℓ) of order k ⩾ n −ℓ−2. We show that none of them satisfies EPC (ℓ) of the same order. We finally give a general construction of nonquadratic functions satisfying EPC (ℓ) of order k . This construction uses the existence of nonlinear, systematic codes with good minimum distances and dual distances (e.g., Kerdock codes and Preparata codes).
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