Some recent results in finite geometry and coding theory arising from the Gale transform

Abstract

The Gale transform is an involution on sets of points in a projective space. It plays a crucial role in several different subjects, such as algebraic geometry, optimization, coding theory, and so on. We give a brief survey—from a finite geometry point of view—on the algebraic and geometrical implications of the Gale transform with emphasis on its applications to coding theory, and describe some recent results.

Keywords

• gale transform
• linear code
• mathieu group
• cap