Biangular Lines Revisited

Abstract

Line systems passing through the origin of the d-dimensional Euclidean space admitting exactly two distinct angles are called biangular. It is shown that the maximum cardinality of biangular lines is at least 2(d-1)(d-2), and this result is sharp for din {4,5,6}. Connections to binary codes, few-distance sets, and association schemes are explored, along with their multiangular generalization.