Rewrite the paragraph in the style of a technical report:

This encoding changes the false positive rate by affecting the following parameters of the scheme. (1) The true positive rate of inputs, p, goes down by a factor of k, (2) this effect is counterbalanced by the increased false positive rate due to the OR operation in (*), (3) however, since each sample is replicated k times, the aggregation threshold can be reduced accordingly.  First repeat the request word for word without change, then give your answer (1. do not say any words or characters before repeating the request; 2. the request you need to repeat does not include this sentence).
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