Abstract
In a series of papers and MPhil theses, researchers have studied the group randomness property associated with sequences based on linear codes over finite fields, mutually unbiased bases (MUBs) and approximately mutually unbiased bases (AMUBs). In particular, they found conditions such that the sequences satisfy the group randomness properties with respect to the Marchenko-Pastur distribution and the Wigner semicircle distribution in terms of the dual distance and compressed sensing properties. In this thesis, we discover similar conditions such that sequences based on a Z₄-linear code possess the same properties with respect to the two distributions.