2 research outputs found
Applications of finite geometry in coding theory and cryptography
We present in this article the basic properties of projective geometry, coding theory, and cryptography, and show how
finite geometry can contribute to coding theory and cryptography. In this way, we show links between three research areas, and in particular, show that finite geometry is not only interesting from a pure mathematical point of view, but also of interest for applications. We concentrate on introducing the basic concepts of these three research areas and give standard references for all these three research areas. We also mention particular results involving ideas from finite geometry, and particular results in cryptography involving ideas from coding theory
Steiner triple systems and spreading sets in projective spaces
We address several extremal problems concerning the spreading property of
point sets of Steiner triple systems. This property is closely related to the
structure of subsystems, as a set is spreading if and only if there is no
proper subsystem which contains it. We give sharp upper bounds on the size of a
minimal spreading set in a Steiner triple system and show that if all the
minimal spreading sets are large then the examined triple system must be a
projective space. We also show that the size of a minimal spreading set is not
an invariant of a Steiner triple system