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In this paper, the spatial properties of high-definition (HD) videos are investigated based on a large set of HD video sequences. Compared with lower resolution videos, the prediction errors of HD videos have higher correlation. Hence, we propose using 2-D order-16 transforms for HD video coding, which are expected to be more efficient to exploit this spatial property, and specifically propose two types of 2-D order-16 integer transforms, nonorthogonal integer cosine transform (ICT) and modified ICT. The former resembles the discrete cosine transform (DCT) and is approximately orthogonal, of which the transform error introduced by the nonorthogonality is proven to be negligible. The latter modifies the structure of the DCT matrix and is inherently orthogonal, no matter what the values of the matrix elements are. Both types allow selecting matrix elements more freely by releasing the orthogonality constraint and can provide comparable performance with that of the DCT. Each type is integrated into the audio and video coding standard (AVS) Enhanced Profile (EP) and the H.264 high profile (HP), respectively, and used adaptively as an alternative to the 2-D order-8 transform according to local activities. At the same time, many efforts have been devoted to further reducing the complexity of the 2-D order-16 transforms and specially for the modified ICT, a fast algorithm is developed and extended to a universal approach. Experimental results show that 2-D order-16 transforms provide significant performance improvement for both AVS enhanced profile and H.264 high profile, which means they can be efficient coding tools especially for HD video coding.