Leveraging the high reactivity, modularity, and orthogonality of the S(VI)-fluoride exchange (SuFEx) reaction, a new addition to click chemistry, we report here the SuFEx iterative exponential growth (SuFEx IEG) method for synthesizing uniform polymers and block copolymers (BCPs) with molecular weights up to 21 kDa. The key step in SuFEx IEG was the on-demand, orthogonal activation of the pair of functional groups, the SuFEx-inactive tetrahydropyranyl and imidazylate groups, into SuFEx-active tert-butyldimethylsilyl (TBS) and sulfonyl fluoride. With SuFEx IEG, we demonstrate the synthetic encoding of 16-bit information into the sequence-defined polysulfate of diphenyl sulfide and diphenyl ether. The modular nature of the SuFEx click reaction enabled the synthesis of uniform polysulfates, including hydrophilic oligo(ethylene glycol)-based polysulfates, that served as modules to create block copolymers (BCPs) and triblock copolymers without molecular weight distribution. The chain ends of the polymers and BCPs produced via SuFEx IEG were used to prepare uniform cyclic polymers and BCPs via intramolecular SuFEx cyclization. The SuFEx IEG method provides a robust and versatile approach for precisely constructing uniform linear and cyclic polymers, as well as sequence-defined polymers, across a broad molecular weight range.