Transmission of short packets in a wireless network is not efficient with classical methods. In fact, most of the available bandwidth is wasted for coordination (network layer), for synchronization (frame header) and for error correction coding (physical layer), leaving little effective throughput rate for data. In this context, the paper proposes a new frame structure called Quasi-Cyclic Short Packet (QCSP) based on the combination of a Cyclic Code Shift Keying (CCSK) modulation and a non-binary error control code. The key idea is to fully exploit the natural cyclic property of the CCSK modulation to perform the frame detection and synchronization in an ALOHA protocol to avoid useless overhead. A theoretical detection model is constructed and used to analyze the detection performance of the frame in very low SNR (from -30 dB to -5 dB). As an example of application, it is shown that a payload of size 120 bits can be transmitted and received correctly with a probability of 99.99% at a signal-to-noise ratio of -9.75 dB, just 1.2 dB from the Polyanskiy's bound (the estimated Shannon limit for small packet size).