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An explicit basis of incidence vectors for the p-ary code of the design of points and hyperplanes of the affine geometry AG m (F p) for any prime p and any integer m ≥ 2 is obtained, which, as a corollary, gives a new elementary proof that this code is a generalized Reed-Muller code. In the proof a class of non-singular matrices related to Vandermonde(More)
We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem. 1. Introduction. In this paper we consider countable mono-unary algebras. A mono-unary algebra used to be defined as a pair A, f where A is a set and f is a unary function from A into A. But here we shall consider a slightly(More)
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