Carlitz rank and additive index cannot be simultaneously small for non-trivial functions over finite fields, complementing prior relations to degree and weight, with a discrete-log example showing all four measures large.
Wang, Cyclotomic mapping permutation polynomials over finite fields
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Additive index and Carlitz rank
Carlitz rank and additive index cannot be simultaneously small for non-trivial functions over finite fields, complementing prior relations to degree and weight, with a discrete-log example showing all four measures large.