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Gap waveguide has recently been proposed as a low-loss and low-cost technology for millimeter-wave components. The main advantage of the gap waveguide technology is that the microwave components can be manufactured in two metallic pieces that are assembled together without electrical contact. The leakage through a thin air gap between the two pieces is prevented by a 2-D periodic structure offering an electromagnetic bandgap (EBG). This EBG is conventionally implemented with metallic pins. Here, we propose the usage of a holey glide-symmetric EBG structure to design a 4 × 4 slot array antenna that is fed with a TE 40 mode. The TE 40 excitation is designed based on a TE 10 -TE 20 mode converter whose performance is initially evaluated by radiation pattern measurements. The final antenna, the 4×4 slot array antenna, was manufactured in aluminum by computer numerical control (CNC) milling. The antenna has a rotationally symmetric radiation pattern that could find application as a reference antenna as well as for 5G point-to-point communications.