The synthesis of thinned isophoric arrays (TIAs) radiating mask-constrained patterns is addressed. By leveraging on the recently-introduced formulation of the design of antenna arrays in the autocorrelation-domain (AD), the TIA synthesis is recast as the matching of a target autocorrelation function derived from the user-defined guidelines and objectives. By exploiting the autocorrelation invariance of cyclic binary sequences, the AD solution space is significantly reduced and it is efficiently sampled by means of a discrete hybrid optimization approach. Two possible implementations of the AD-based TIA formulation are discussed and assessed in a set of representative numerical examples concerned with both ideal and real radiators, which are full-wave modeled to account for the mutual coupling effects. Comparisons with traditional pattern-domain (PD) synthesis methods are also considered to point out the features and the advantages of AD-based approaches.