Abstract
We describe a simple procedure for constructing Steiner 2-designs with the parameters of the designs of points and lines of a finite projective or affine geometry of dimension m⩾3; the codes of many of the designs constructed in this way will contain the code of the relevant finite-geometry design (a Reed-Muller or generalized Reed-Muller code). The designs can be extended to 3-designs provided that planes in the finite-geometry design extend.
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