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Hyperdimensional computing (HDC) is an emerging computing paradigm that represents, manipulates, and communicates data using very long random vectors (aka hypervectors). Among different hardware platforms capable of executing HDC algorithms, in-memory computing (IMC) systems have been recently proved to be one of the most energy-efficient options, due to hypervector manipulations in the memory itself that reduces data movement. Although implementations of HDC on single IMC cores have been made, their parallelization is still unresolved due to the communication challenges that these novel architectures impose and that traditional Networks-on-Chip and Networks-in-Package were not designed for. To cope with this difficulty, we propose the use of wireless on-chip communication technology in unique ways. We are particularly interested in physically distributing a large number of IMC cores performing similarity search across a chip, and maintaining the classification accuracy when each of which is queried with a slightly different version of a bundled hypervector. To achieve it, we introduce a novel over-the-air computing that consists of defining different binary decision regions in the receivers so as to compute the logical majority operation (i.e., bundling, or superposition) required in HDC. It introduces moderate overheads of a single antenna and receiver per IMC core. By doing so, we achieve a joint broadcast distribution and computation with a performance and efficiency unattainable with wired interconnects, which in turn enables massive parallelization of the architecture. It is demonstrated that the proposed approach allows to both bundle at least three hypervectors and scale similarity search to 64 IMC cores seamlessly, while incurring an average bit error ratio of 0.01 without any impact in the accuracy of a generic HDC-based classifier working with 512-bit vectors.