The advancement in multimedia-based applications has sustained the need for more efficient ways to encode signals and images. Over the years, the Discrete Cosine Transform (DCT) has emerged as the most popular transform for many image and video coding applications. While implementing the DCT using finite-precision, approximation of the real-valued transform coefficients is required. It not only results in computational error, but also limits the quality of the reconstruction. An error-free encoding using algebraic integers has been shown to be an effective way of resolving the issue. The...