Abstract
In bose&burton, Bose and Burton determined the smallest point sets of PG(d, q) that meet every subspace of PG(d, q) of a given dimension c. In this paper an equivalent result for quadrics of elliptic type is obtained. It states the folloing. For 0 ≤ c ≤ n - 1 the smallest point set of the elliptic quadric Q -(2n + 1, q) that meets every singular subspace of dimension c of Q -(2n + 1, q) has cardinality (q n+1 + q c)(q n-c - 1)/(q - 1). Furthermore, the point sets of the smallest cardinality are classified.
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Metsch, K. A Bose-Burton Theorem for Elliptic Polar Spaces. Designs, Codes and Cryptography 17, 219–224 (1999). https://doi.org/10.1023/A:1026483311192
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DOI: https://doi.org/10.1023/A:1026483311192