Traffic data exhibits complex temporal, spatial, and spatial-temporal correlations. Most of models use either independent modules to separately extract temporal and spatial correlations or joint modules to synchronously extract them, without considering the spatial-temporal correlations. Moreover, models that consider joint spatial-temporal correlations (temporal, spatial, and spatial-temporal correlations) often encounter significant challenges in accuracy and computational efficiency which prevent such models from demonstrating the expected advantages of a joint spatial-temporal correlations architecture. To address these issues, this paper proposes an efficient pure convolutional network for traffic prediction via spatial-temporal encoding and inferring (STEI-PCN). The model introduces and designs a dynamic adjacency matrix inferring module based on absolute spatial and temporal coordinates, as well as relative spatial and temporal distance encoding, using a graph convolutional network combined with gating mechanism to capture local synchronous joint spatial-temporal correlations. Additionally, three layers of temporal dilated causal convolutional network are used to capture long-range temporal correlations. Finally, through multi-view collaborative prediction module, the model integrates the gated-activated original, local synchronous joint spatial-temporal, and long-range temporal features to achieve comprehensive prediction. This study conducts extensive experiments on flow datasets (PeMS03/04/07/08) and speed dataset (PeMS-Bay), covering multiple prediction horizons. The results show that STEI-PCN demonstrates competitive computational efficiency in both training and inference speeds, and achieves superior or slightly inferior to state-of-the-art (SOTA) models on most evaluation metrics.