On the trellis representation of the Delsarte-Goethals codes

In this correspondence, the trellis representation of the Kerdock and Delsarte-Goethals codes is addressed. It is shown that the states of a trellis representation of DG(m,/spl delta/) under any bit-order are either strict-sense nonmerging or strict-sense nonexpanding, except, maybe, at indices within the code's distance set. For /spl delta//spl ges/3 and for m/spl ges/6, the state complexity, s/sub max/[DG(m,/spl delta/)], is found. For all values of m and /spl delta/, a formula for the number of states and branches of the biproper trellis diagram of DG(m, /spl delta/) is given for some of the indices, and upper and lower bounds are given for the remaining indices. The formula and the bounds refer to the Delsarte-Goethals codes when arranged in the standard bit-order.