This work compares the performances of two Golomb family entropy coders applied to a video codec system named FHVC (fast hadamard video codec). The entropy coders considered have different operation modes and specific adaptation strategies. The work also presents a new 3D-transform coefficient scan order developed for the FHVC. This scan process is based on the multiplication of the three-dimensional sequency numbers of each coefficient. The FHVC (which is also described in this work) is a fast embedded color video codec developed to be implemented in a video set-top box used in a fiber optics network. The focus is on more reduced execution times, and not on higher compression rates. Low computational complexity and use of meager computational resources are also required. All the multiplications and divisions operations are performed by binary shifts and the system is implemented exclusively with 16-bit integer arithmetic. Even with these constraints, good distortion versus bit-rate results were achieved. The Hadamard transform is used in a three-dimensional fashion, in order to reduce spatial and temporal correlation and to avoid costly motion estimation and compensation techniques. The proposed scan procedure allows the transform coefficient reading in an idealistic ''decreasing in the average'' order. After the scan procedure, the encoding of the bit sequence of the 3D-Hadamard coefficients is carried out, bit-plane-by-bit-plane, with an adaptive Golomb run-length entropy coder, which produces a fully embedded output bitstream. Two entropy coders were considered. The first one uses an empirical, but fast and efficient, adaptation strategy that shows good results on non-stationary data. The second one has an adaptation strategy that is nearly optimum, in a maximum-likelihood sense, for independent Bernoulli identically distributed data.