Rahilly [10] described a construction that relates any Hadamard design H on 4m−1 points with a line spread to an affine design having the same parameters as the classical design of points and hyperplanes in AG(m, 4). Here it is proved that the affine design is the classical design of points and hyperplanes in AG(m, 4) if, and only if, H is the classical design of points and hyperplanes in PG(2m...

The hyperplanes of the symplectic dual polar space DW (5, q) arising from embedding, the so-called classical hyperplanes of DW (5, q), have been determined earlier in the literature. In the present paper, we classify non-classical hyperplanes of DW (5, q). If q is even, then we prove that every such hyperplane is the extension of a non-classical ovoid of a quad of DW (5, q). If q is odd, then w...

Abstract Problems such as data compression, pattern recognition and artificial intelligence often deal with a large sample observations of an unknown object. An effective method is proposed to fit hyperplanes points in each hypercubic subregion the original sample. Corresponding set affine linear manifolds, locally fitted optimally approximate object sense least squares their perpendicular dist...

It is proved that the collection of blocks of an affine 1-design that yields a linear orthogonal array is a union of parallel classes of hyperplanes in a finite affine space. In particular, for every prime power q and every m ≥ 2 there exists a unique (up to equivalence) complete linear orthogonal array of strength two associated with the classical design of points and hyperplanes in AG(m, q).