The number of directions determined by a function over a finite field

Authors:
Simeon Ball
Affiliations:
Department of Mathematics, Queen Mary College, University of London, London E1 4NS, UK
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

Citing 3
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Abstract

A proof is presented that shows that the number of directions determined by a function over a finite field GF(q) is either 1, at least (q + 3)/2, or between q/s + 1 and (q - 1)/(s - 1) for some s where GF(s) is a subfield of GF(q). Moreover, the graph of those functions that determine less than half the directions is GF(s)-linear. This completes the unresolved cases s = 2 and 3 of the main theorem in Blokhuis et al. (J. Combin. Theory Ser. A 86 (1999) 187).