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, 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 delta greater than or e qual to 3 and for m greater than or equal to 6, the slate complexity, s(max) [DG(m, delta)], is found. For all values of m and delta, a form ula for the number of states and branches of the biproper trellis diag ram of DG(m, delta) is given for some of the indices, and upper and lo wer bounds are given for the remaining indices. The formula and the bo unds refer to the Delsarte-Goethals codes when arranged in the standar d bit-order.