✦ LIBER ✦

Linear independence in finite spaces

✍ Scribed by J. W. P. Hirschfeld; J. A. Thas

Publisher: Springer
Year: 1987
Tongue: English
Weight: 633 KB
Volume: 23
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00147388

No coin nor oath required. For personal study only.

✦ Synopsis

The maximum number m2 (n , q) of points in PG(n, q), n >~ 2, such that no three are collinear is known precisely for (n, q) = (n, 2), (2, q), (3, q), (4, 3), (5, 3). In this paper an improved upper bound of order q"-1 _ ½q,-2 is obtained for q even when n >~ 4 and q > 2. A necessary preliminary is an improved upper bound for m~(3, q),. the maximum size of a k-cap not contained in an ovoid. It is shown that rn~(3, q) ~< qZ _ ½q _ ½x/q + 2 and that m~(3, 4) = 14.

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