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Many image or video coding standards that are based on discrete cosine transform (DCT) rely on a step size matrix to normalize the DCT coefficients prior to quantization. The JPEG lossy image coding standard, for example, transmits the step size matrix as part of the bit-stream. In this study we present several low complexity lossless and lossy compression schemes that are applicable to the step size matrix, these schemes do not introduce any distortion to the decoded image data, and can be used in transcoding or to provide additional compression in storage applications. Experimental results show that on average the step size matrix of a JPEG file can be stored using 29% of the original bit requirement.