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Equality operators are an essential building block in tasks over secure computation such as private information retrieval. In private information retrieval (PIR), a user queries a database such that the server does not learn which element is queried. In this work, we propose \emph{equality operators for constant-weight codewords}. A constant-weight code is a collection of codewords that share the same Hamming weight. Constant-weight equality operators have a multiplicative depth that depends only on the Hamming weight of the code, not the bit-length of the elements. In our experiments, we show how these equality operators are up to 10 times faster than existing equality operators. Furthermore, we propose PIR using the constant-weight equality operator or \emph{constant-weight PIR}, which is a PIR protocol using an approach previously deemed impractical. We show that for private retrieval of large, streaming data, constant-weight PIR has a smaller communication complexity and lower runtime compared to SEALPIR and MulPIR, respectively, which are two state-of-the-art solutions for PIR. Moreover, we show how constant-weight PIR can be extended to keyword PIR. In keyword PIR, the desired element is retrieved by a unique identifier pertaining to the sought item, e.g., the name of a file. Previous solutions to keyword PIR require one or multiple rounds of communication to reduce the problem to normal PIR. We show that constant-weight PIR is the first practical single-round solution to single-server keyword PIR.