On the number of rational points on codimension-1 algebraic sets in Pn(Fq) Original Research Article

An upper bound on the number of Fq-rational points on a pure (n - 1)-dimensional algebraic set of low degree defined over Fq in Pn(Fq) is given, using simple counting arguments, and the result is generalized to all degrees using results from coding theory. The bound depends on n, q, d, where d is the degree of the algebraic set. A number of corollaries are deduced and applications to coding theory are mentioned.