Abstract: A method of design and implementation of trellis codes for intersymbol interference channels is provided wherein a set of input vectors is mapped to a set of output vectors comprising the steps of forming a minimized basis having a set of minimized basis vectors configured for a set of channel output signals corresponding to the set of output vectors; selecting the smallest member of the set of minimized basis vectors as a coset vector; forming a partition basis by adding the coset vector to at least one member of the set of the minimized basis vectors; and forming a subsequent minimized basis from the partition basis. These codes circumvent the necessity for intersymbol interference removal, thereby reducing equalization complexity.