Tight wavelet frame sets in finite vector spaces

Let q≥2 be an integer, and Fqd, d≥1, be the vector space over the cyclic space Fq. The purpose of this paper is two-fold. First, we obtain sufficient conditions on E⊂Fqd such that the inverse Fourier transform of 1E generates a tight wavelet frame in L2(Fqd). We call these sets (tight) wavelet frame sets. The conditions are given in terms of multiplicative and translational tilings, which is analogous with Theorem 1.1 ([20]) by Wang in the setting of finite fields. In the second part of the paper, we exhibit a constructive method for obtaining tight wavelet frame sets in Fqd, d≥2, q an odd prime and q≡3 (mod 4).