Small weight codewords in the dual code of points and hyperplanes in PG(n, q), q even

Abstract

The main theorem of this article gives a classification of the codewords in $${C^{\bot}_{n-1}(n,q)}$$ , the dual code of points and hyperplanes in PG(n, q), q even, with weight smaller than $${q+\sqrt[3]{q^{2}}+1}$$ . In the proof, we rely on the classification of the small blocking sets in PG(2, q), q even.