With the rapid popularity of short video applications, a large number of short video transmissions occupy the bandwidth, placing a heavy load on the Internet. Due to the extensive number of short videos and the predominant service for mobile users, traditional approaches (e.g., CDN delivery, edge caching) struggle to achieve the expected performance, leading to a significant number of redundant transmissions. In order to reduce the amount of traffic, we design a Novel Coded Transmission Mechanism (NCTM), which transmits XOR-coded data instead of the original video content. NCTM caches the short videos that users have already watched in user devices, and encodes, multicasts, and decodes XOR-coded files separately at the server, edge nodes, and clients, with the assistance of cached content. This approach enables NCTM to deliver more short video data given the limited bandwidth. Our extensive trace-driven simulations show how NCTM reduces network load by 3.02%-14.75%, cuts peak traffic by 23.01%, and decreases rebuffering events by 43%-85% in comparison to a CDN-supported scheme and a naive edge caching scheme. Additionally, NCTM also increases the user's buffered video duration by 1.21x-13.53x, ensuring improved playback smoothness.