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We present a new class of private information retrieval (PIR) schemes thatkeep the identity of the file requested private in the presence of at most $t$colluding servers, based on the recent framework developed for such $t$-PIRschemes using star products of transitive codes. These $t$-PIR schemes employthe class of Berman codes as the storage-retrieval code pairs. Berman codes,which are binary linear codes of length $n^m$ for any $n\geq 2$ and $m\geq 1$being positive integers, were recently shown to achieve the capacity of thebinary erasure channel. We provide a complete characterization of the starproducts of the Berman code pairs, enabling us to calculate the PIR rate of thestar product-based schemes that employ these codes. The schemes we present haveflexibility in the number of servers, the PIR rate, the storage rate, and thecollusion parameter $t$, owing to numerous codes available in the class ofBerman codes.

$t$-PIR Schemes with Flexible Parameters via Star Products of Berman Codes