Some new two-weight codes and strongly regular graphs

AbstractIt is well known (and due to Delsarte [3]) that the three concepts (i) two-weight projective code, (ii) strongly regular graph defined by a difference set in a vector space, and (iii) subset X of a projective space such that |X∩H| takes only two values when H runs over all hyperplanes, are equivalent. Here we construct some new examples (formulated as in (iii)) by taking a quadric defined over a small field and cutting out a quadratic defined over a larger field