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2008
IEEE

On the graph of a function in many variables over a finite field

9 years 2 months ago
On the graph of a function in many variables over a finite field
Some improved bounds on the number of directions not determined by a point set in the affine space AG(k, q) are presented. More precisely, if there are more than pe (q -1) directions not determined by a set of qk-1 points S then every hyperplane meets S in 0 modulo pe+1 points. This bound is shown to be tight in the case pe = qs and when q = pes sets of qk-1 points that do not meet every hyperplane in 0 modulo pe+1 points and have a little less than pe (q - 1) non-determined directions are constructed.
Simeon Ball
Added 25 Dec 2009
Updated 25 Dec 2009
Type Conference
Year 2008
Where DCC
Authors Simeon Ball
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