Abstract: A Galois field linear transformer trellis system includes a Galois field linear transformer matrix; an input selection circuit for providing to the matrix a number of input bits in one or more trellis bit streams and a trellis state output of the matrix and a programmable storage device for configuring the matrix to perform a multi-cycle Galois field transform of the one or more trellis bit steams and trellis state output to provide a plurality of trellis output channel symbols and a new trellis state output in a single cycle.