The Power of Desarguesian Sets

Abstract

A Desarguesian set is a planar Euclidean geometry difference set which can be used to derive new cyclic block codes, convolutional self-orthogonal codes, and random multiple access codes. This paper discusses the usefulness of these codes and presents the step-by-step procedure for the purpose of constructing such sets. Comparisons are also made with planar projective geometry sets in which two types of existing codes were obtained.