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...ty. We give minimal span generator matrices (MSGMs) for these codes with an application to parallelism in uniform sectionalisations of their minimal trellises. The results generalise some of those in =-=[2]-=-. Generalised Reed{Muller codes We denote thesniteseld with q elements by F q . We put P q (m) equal to those polynomials in F q [X 1 ; : : : ; Xm ] of degree no more than q 1 in each variable and for...

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...nother way, the branch complexity of the minimal trellis representation of RM(r,m) in the standard bit order attains the lower bound on, and thus equals, the trelliswidth of the code. Techniques from =-=[2]-=- allow us to compute, with very little effort, the branch complexity of this trellis representation. We give the details of this computation in Appendix A. From this, we obtain the following result. 6...