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In this paper we continue a classical work of Sch\"utzenberger on codes withbounded synchronization delay. He was interested to characterize those regularlanguages where the groups in the syntactic monoid belong to a variety $H$. Heallowed operations on the language side which are union, intersection,concatenation and modified Kleene-star involving a mapping of a prefix code ofbounded synchronization delay to a group $G\in H$, but no complementation. Inour notation this leads to the language classes $SD_G(A^\infty)$ and$SD_H(A^\infty$). Our main result shows that $SD_H(A^\infty)$ alwayscorresponds to the languages having syntactic monoids where all subgroups arein $H$. Sch\"utzenberger showed this for a variety $H$ if $H$ contains Abeliangroups, only. Our method shows the general result for all $H$ directly onfinite and infinite words. Furthermore, we introduce the notion of local Reesproducts which refers to a simple type of classical Rees extensions. We give adecomposition of a monoid in terms of its groups and local Rees products. Thisgives a somewhat similar, but simpler decomposition than in Rhodes' synthesistheorem. Moreover, we need a singly exponential number of operations, only.Finally, our decomposition yields an answer to a question in a recent paper ofAlmeida and Kl\'ima about varieties that are closed under Rees products.

Characterizing classes of regular languages using prefix codes of bounded synchronization delay