This work of thesis shows a new factorization and its implementation for DCT-V(Discrete Cosine Transform) of length 4 and 32, used in the most recent video compression standard. During the last years, the Joint Video Exploration Team(JVET) of ITU-T VCEG and ISO/IEC MPEG, now the Joint Video Experts Team, are trying to develop the future video coding technology, that will improve the compression efficiency with respect to the current HEVC standard. An experimental software was introduced, JEM, based on the HEVC Model (HM) software, developed as reference for the HEVC standard. One of the fundamental data compression techniques used for this standard, as in many previous image and video coding standards, is transform coding.