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This brief is concerned with the efficient and error-free implementation of the order-8 Linzer-Feig (L-F) scaled discrete cosine transform (sDCT). We present a novel 3-D algebraic integer encoding scheme which maps the transform basis functions (transcendental functions such as cosine and tangent) with integer values, so that the quantization errors can be minimized and the cross-multiplications (in the signal path) can be avoided. This scheme also allows the separable computation of a 2-D DCT in multiplication-free, fast, and efficient architectures with a process rate of 80 mega-samples/sec. The proposed scheme also reduces the latency and the power consumption compared to previously employed designs for DCT implementations.