A speech/audio codec based on Frequency Domain Linear Prediction (FDLP) exploits auto-regressive modeling to approximate instantaneous energy in critical frequency sub-bands of relatively long input segments. The current version of the FDLP codec operating at 66 kbps has been shown to provide comparable subjective listening quality results to state-of-the-art codecs on similar bit-rates even without employing standard blocks such as entropy coding or simultaneous masking. This paper describes an experimental work to increase compression efficiency of the FDLP codec by employing entropy coding. Unlike conventional Huffman coding employed in current speech/audio coding systems, we describe an efficient way to exploit arithmetic coding to entropy compress quantized spectral magnitudes of the sub-band FDLP residuals. Such an approach provides 11\% ( 3 kbps) bit-rate reduction compared to the Huffman coding algorithm ( 1 kbps).