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,δ) under any bit-order are either strict-sense nonmerging or strict-sense nonexpanding, except, maybe, at indices within the code´s distance set. For δ⩾3 and for m⩾6, the state complexity, s_max[DG(m,δ)], is found. For all values of m and δ, a formula for the number of states and branches of the biproper trellis diagram of DG(m, δ) 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