Let q = 2 be an integer, and F-q(d), d = 1, be the vector space over the cyclic space F-q. The purpose of this paper is two-fold. First, we obtain sufficient conditions on E subset of F-q(d), such that the inverse Fourier transform of 1(E) generates a tight wavelet frame in L-2(F-q(d)). 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 F-q(d), d = 2, q an odd prime and q equivalent to 3 (mod 4). (C) 2017 Published by Elsevier Inc.
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