Photoacoustic (PA) imaging is an emerging imaging technology combining optical imaging with ultrasound. There has been a strong demand for PA flow imaging of contrast agents such as blood or nano-particles for observing the disease process or drug delivery. In conventional PA flow imaging, however, the temporal resolution is limited by the acoustic time-of-flight (TOF), which is the highest possible frame rate, and the sensitivity is determined by the signal-to-noise ratio (SNR). We propose coded excitation using periodic pseudorandom sequences to achieve PA flow imaging with high sensitivity and ultra-high temporal resolution beyond that of acoustic TOF. A periodically and unipolarly implemented m-sequence was chosen as the code for coded excitation. The frame-rate, which was limited by the acoustic TOF, can be maximized up to the pulse repetition frequency since the start point of decoding can be set in any code in the periodic sequence. Therefore, velocities can be acquired at shorter intervals, and higher temporal resolution is achieved. Moreover, the SNR can be improved by compressing coded signals. We demonstrate the feasibility through experiments. Coding significantly improved the SNR, so that the estimated velocity agreed well with the true designated velocity. In addition, we confirmed a shorter interval of temporal velocity change from the coded results. This indicates that slight flow variations, which could not be observed without coding, can be detected.