Several new constructions of mutually unbiased bases derived from functions over finite fields.

A collection B = { B 1 , B 2 , ⋯ , B N } of orthonormal bases of C K is called mutually unbiased bases if | ⟨ v i | v j ⟩ | = 1 K for all v i ∈ B i , v j ∈ B j and 1 ≤ i < j ≤ N . In this paper, we present several new series of mutually unbiased bases constructed by utilizing p-ary weakly regular bent functions, permutation polynomials and PN functions over finite fields. Specifically, we are the first to use weakly regular bent functions to construct MUBs. In addition, we obtain a complete set of MUBs by employing linearized permutation polynomials over finite fields. [ABSTRACT FROM AUTHOR]